Multiple choice questions_in_engineering_mathematics_by_venancio_i._besavilla__jr._vol2.doc

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ENGINEERING MATHEMATICS BY BESAVILLA VOL 2
MULTIPLE CHOICE QUESTIONS IN
ENGINEERING MATHEMATICS
FOR
COMPUTERIZED LICENSURE EXAM
Author:
Venancio I. Besavilla, Jr.
Engineering Economics
1.) A price tag of P1200 is specified if paid within 60 days but offers a 3%
discount for cash in 30 days. Find the rate of interest.
a.37.11% c. 40.21%
b.38.51% d. 39.31%
2.) It is the practice of almost all bank in the Philippines that when they grant a
loan, the interest for 1 year is automatically deducted from the principal amount
upon release of money to a borrower. Let us therefore assume that you applied for
a loan with the bank and the P80000 was approved at an interest rate of 14% of
which P11200 was deducted and you were given ac check of P68800. Since you
have to pay the amount of P80000 one year after, what then will be the effective
interest rate?
a.16.28% c. 17.30%
b.38.51% d. 39.31%
3.) Mr. J. Dela Cruz borrowed money from the bank. He received from the bank
P1,340.00 and promised to pay P1,500.00 at the end of 9 months. Determine the
simple interest rate and the corresponding discount rate or often referred to as the
“Banker’s Discount”.
a.15.92% ; 13.73% c. 12.95% ; 17.33%
b.18.28% ; 13.12% d. 19.25% ;
13.33%
4.) A man borrowed from the bank under a promissory note that he signed in the
amount of P25000.00 for a period of 1year. He received only the amount of
P21,915.00 after the bank collected the advance interest and an additional amount
of P85.00 for notarial and inspection fees. What was the rate of interest that the
bank collected in advance?
a.13.64% c. 16.43%
b.18.37% d. 10.32%
5.) Agnes Abanilla was granted a loan of P20,000 by her employer CPM Industrial
Fabricator and Construction Corporation with an interest at 6% for 180days on the
principal collected in advance. The corporation would accept a promissory note for
P20,000 non-interest for 180days. If discounted at once, find the proceeds in the
note.
a. P18,800 c. P18,000
b. P19,000 d. P18,400
6.) P4000 is borrowed for 75days at 16% per annum simple interest. How much
will be due at the end of 75days?
a. P4186.43 c. P4133.33
b. P5124.54 d. P5625.43
7.) Mr. Almagro made a money market placement of P1,000,000 for 30 days at
7.5% per year. If withholding tax is 20%, what is the net interest that Mr. Almagro
will receive at the end of the month?
a. P3,000 c. P6,000
b. P4,000 d. P5,000
8.) A bill for motorboat specifies the cost as P1,200 due at the end of 100days but
offers a 4% discount for cash in 30days. What is the highest rate, simple interest at
which the buyer can afford to borrow money in order to take advantage of the
discount?
a. 18.4% c. 20.9%
b. 19.6% d. 21.4%
9.) In buying a computer disk, the buyer was offered the options of paying P250
cash at the end of 30days or P270 at the end of 120days. At what rate is the buyer
paying simple interest if he agree to pay at the end of 120days?
a. 32% c. 28%
b.40% d. 25%
10.) On March 1, 1996 Mr. Almagro obtains a loan of P1500 from Mr. Abella and
signs a note promising to pay the principal and accumulated simple interest at the
rate of 5% at the end of 120days. On May 15, 1996, Mr. Abella discounts the note
at the bank whose discount rate is 6%. What does he receive?
a. P2,201.48 c. P1,513.56
b. P1,123.29 d. P938.20
11.) A deposit of P110,000 was made for 31days. The net interest after deducting
20% withholding tax is P890.36. Find the rate of return annually.
a. 12.25 c. 12.75
b. 11.75 d. 11.95
12.) If you borrowed money from your friend with simple interest of 12%, find the
present worth of P50,000 which is due at the end of 7months.

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a. P46,200 c. P46,729
b. P44,893 d. P45,789
13.) A man borrowed P2000 from a bank and promise to pay the amount for 1year.
He received only the amount of P1,920 after the bank collected an advance interest
of P80. What was the rate of discount and the rate of interest that the bank
collected in advance?
a. 4% ; 4.17% c. 4% ; 4.71%
b. 3% ; 3.17% d. 3% ; 3.71%
14.) An engineer promised to pay P36,000 at the end of 90days. He was offered a
10% discount if he pays in 30days. Find the rate of interest.
a. 64.6% c. 66.6%
b. 65.6% d. 67.6%
15.) A man is required to pay P200 at the end of 160days or P190 at the end of
40days. Determine the rate of interest.
a. 18.4% c. 15.8%
b. 19.6% d. 16.4%
16.) Compute the discount if P2000 is discounted for 6months at 8% simple
interest.
a. P29.67 c. P76.92
b. P67.29 d. P92.76
17.) The amount of P12800 in 4years at 5% compounded quarterly is _____.
a. P14,785.34 c. P16,311.26
b. P15,614.59 d. P15,847.33
18.) A man borrows money from a bank which uses a simple discount rate of 14%.
He signs a promissory note promising to pay P500.00 per month at the end of 4th
,
6th
, and 7th
month respectively. Determine the amount of money that he received
from the bank.
a. P1403.68 c. P1102.37
b. P1340.38 d. P1030.28
19.) A nominal interest of 3% compounded continuously is given on the account.
What is the accumulated amount of P10,000 after 10years?
a. P13,610.10 c. P13,498.60
b. P13,500.10 d. P13,439.16
20.) BY the condition of a will, the sum of P2000 is left to a girl to be held in trust
fund by her guardian until it amount to P50000.00. When will the girl receive the
money of the fund is invested at 8% compounded quarterly?
a. 7.98 years c. 11.57 years
b. 10.34 years d. 10.45 years
21.) A man expects to receive P25,000 in 8 years. How much is that worth now
considering interest at 8% compounded quarterly?
a. P13,859.12 c. P13,675.23
b. P13,958.33 d. P13,265.83
22.) P500,000 was deposited at an interest of 6% compounded quarterly. Compute
the compound interest after 4 years and 9 months.
a. P163,475.37 c. P158,270.37
b. P178,362.37 d. P183,327.37
23.) If the nominal interest rate is 3%, how much is P5000 worth in 10 years in a
continuously compounded account?
a. P5750 c. P7500
b. P6750 d. P6350
24.) P200,000 was deposited for a period of 4 years and 6 months and bears on
interest of P85649.25. What is the rate of interest if it is compounded quarterly?
a. 8% c. 7%
b. 6% d. 5%
25.) How many years will P100,000 earn a compound interest of P50,000 if the
interest rate is 9% compounded quarterly?
26.) A certain amount was deposited 5 years and 9 months ago at an interest of 8%
compounded quarterly. If the sum now is P315,379.85, how much was the amount
deposited?
a. P200,000 c. P240,000
b. P180,000 d. P260,000

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For Problems 27-29:
When compounded Bi-monthly, P15000 becomes P22,318.30 after 5years.
27.) What is the nominal rate of interest?
a. 7% c. 9%
b. 8% d. 10%
28.) What is the equivalent rate if it is compounded quarterly?
a. 7.03% c. 9.03%
b. 8.03% d. 10.03%
29.) What is the effective rate if it is compounded quarterly?
a. 7.28% c. 9.28%
b. 8.28% d. 10.28%
30.) How will it take a money to double itself if invested at 5% compounded
annually?
a. 12.2 years c.
14.2 years
b. 13.2 years d.
15.2years
31.) Compute the effective annual interest rate which is equivalent to 5% nominal
annual interest compounded continuously.
a. 5.13% c. 5.26%
b. 4.94% d. 4.90%
32.) Find the time required for a sum of money to triple itself at 5% per annum
compounded continuously.
33.) A man wishes to have P40,000 in a certain fund at the end of 8 years. How
much should he invest in a fund that will pay 6% compounded continuously?
a. P24,751.34 c. P28,864.36
b. P36,421.44 d. P30,468.42
34.) If the effective annual interest rate is 4%, compute the equivalent nominal
annual interest compounded continuously.
a. 3.92% c. 3.80%
b. 4.10% d. 4.09%
35.) What is the nominal rate of interest compounded continuously for 10 years if
the compound amount factor is equal to 1.34986?
a. 3% c. 5%
b. 4% d. 6%
36.) American Express Corp. charges 1.5% interest per month, compounded
continuously on the unpaid balance purchases made on this credit card. Compute
the effective rate of interest.
a. 19.72% c. 21.20%
b. 20.25% d. 19.90%
37.) If the nominal interest is 12% compounded continuously, compute the
effective annual rate if interest.
a. 12.75% c. 12.40%
b. 11.26% d. 11.55%
38.) Compute the difference in the future amount of P500 compounded annually at
nominal rate of 5% and if it is compounded continuously for 5 years at the same
rate.
a. P3.87 c. P5.48
b. P4.21 d. P6.25
39.) If the effective rate is 24%, what nominal rate of interest is charged for a
continuously compounded loan?
a. 21.51% c. 23.25%
b. 22.35% d. 21.90%
40.) What is the nominal rate of interest compounded continuously for 8 years if
the present worth factor is equal to 0.6187835?
a. 4% c. 6%
b. 5% d. 7%
41.) What is the difference of the amount 3 years from now for a 10% simple
interest and 10% compound interest per year?(P5000 accumulated)

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a. P155 c. same
b. P100 d. P50
42.) Find the discount if P2,000 is discounted for 6 months at 8% compounded
quarterly.
a. P76.92 c. P77.66
b. P80.00 d. P78.42
43.) If a sum of money triples in a certain period of time at a given rate interest,
compute the value of the single payment present worth factor.
a. 0.333 c. 0.292
b. 3.000 d. 1.962
44.) If the single payment amount factor for a period of 5 years is 1.33822. What is
the nearest value of the interest rate?
a. 8% c. 5%
b. 7% d. 6%
45.) If the single payment present worth factor for a period of 8 years is equal to
0.58201, compute the nearest value of the rate of interest for that period.
a. 6% c. 5%
b. 7% d. 8%
46.) If money is worth 8% compounded quarterly, compute the single payment
amount factor for a period of 6 years.
a. 1.60844 c. 1.70241
b. 0.62172 d. 0.53162
47.) A sum of P1,000 is invested now and left for 8 years, at which time the
principal is withdrawn. The interest has an accrued left for another 8 years. If the
effective annual interest is 5%, what will be the withdrawn amount at the end of
the 16th
year?
a. P507.42 c. P750.42
b. P705.42 d. P425.07
For problems 48-50:
Compute the interest for an amount of P200,000 for a period of 8 years.
48.) If it was made at a simple interest rate of 16% .
a. P274,000 c.
P256,000
b. P265,000 d.
P247,000
49.) If it was made at 16% compounded bi-monthly.
a. P507,267.28 c. P407,283.01
b. P507,365.96 d. P459,923.44
50.) If it was made at 16% compounded continuously.
a. P422,462.64 c. P524,242.46
b. P507,233.24 d. P519,327.95
51.) Find the value of x, (F/P, x, 6) if F/P compounded quarterly is equal to
1.612226.
a. 7% c. 5%
b. 8% d. 6%
52.) Find the value of y, (P/F, 6%, y) if P/F compounded bi-monthly is equal to
0.787566.
a. 7 years c. 5 years
b. 6 years d. 4 years
53.) Find the rate of interest if compound amount factor compounded bi-monthly
for 5 years is equal to 1.487887.
a. 7% c. 5%
b. 8% d. 6%
54.) Compute the nominal rate for a period of 6 years for an effective rate of
8.33% if it is compounded continuously.
a. 7% c. 5%
b. 8% d. 6%
55.) Compute the equivalent compound amount factor if it is compounded
continuously.
a. 1.61607 c. 1.24532
b. 1.24282 d. 0.24245

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56.) Compute the equivalent present worth factor if it is compounded continuously.
a. 1.249347 c. 1.243248
b. 1.214359 d. 0.616783
57.) A man loan P2000 from the bank. How long would it take in years for the
amount of the loan and interest to equal P3280 if it was made at 8% simple
interest.
58.) A man loan P2000 from the bank. How long would it take in years if it was
made at 8% compounded quarterly.
59.) A man loan P2000 from the bank. How long would it take in years if it was
made at 8% compounded continuously.
60.) An amount of P1000 becomes P1608.44 after 4 years compounded bi-
monthly. Find the nominal rate of interest, the effective rate of interest, and the
equivalent rate of interest if it is compounded quarterly.
a. 11% ; 12.623% ; 11.42% c. 12% ; 11.06% ;
12.724%
b. 12% ; 12.616% ; 12.06% d. 11% ; 11.664% ;
11.93%
61.) How long would it take your money to double itself if it is invested at 6%
simple interest, compounded semi-quarterly, and compounded continuously?
a. 12.67yrs ; 11.2yrs ; 15.05yrs c. 18.67yrs ; 11.6yrs ; 11.24yrs
b. 16.67yrs ; 11.6yrs ; 11.55yrs d. 17.67yrs ; 10.2yrs ; 11.45yrs
For problems 62-64:
An amount of P50,000 was invested for 3 years.
62.) Compute its interest at the end of 3 years if it is invested at 10% simple
interest.
a. P16,550.00 c. P15,000.00
b. P17,492.94 d. P14,242.15
63.) Compute for its compound interest if it is invested at 10% compounded
annually.
a. P16,550.00 c. P15,000.00
b. P17,492.94 d. P14,242.15
64.) Compute its interest if it is invested at 10% compounded continuously.
a. P16,550.00 c. P15,000.00
b. P17,492.94 d. P14,242.15
For Problems 65-67:
P200,000 was deposited for a period of 4 yrs. And 6 months and bears on interest
of P85,659.25.
65.) What is the nominal rate of interest if it is compounded quarterly?
a. 8.00% c. 7.00%
b. 8.24% d. 7.96%
66.) What is the actual rate of interest?
a. 8.00% c. 7.00%
b. 8.24% d. 7.96%
67.) What is the equivalent nominal rate if it is compounded semi-quarterly?
a. 8.00% c. 7.00%
b. 8.24% d. 7.96%
68.) What is the value of (F/P, 8%, 6) if it is compounded semi-quarterly.
a. 0.524273541 c. 1.487886717
b. 0.787566127 d. 1.612226000
69.) What is the value of (P/F, 6%, 4) if it is compounded bi-monthly.
a. 0.524273541 c. 1.487886717
b. 0.787566127 d. 1.612226000
70.) What is the single payment compound amount factor for 8% compounded bi-
monthly for 5 years.

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a. 0.524273541 c. 1.487886717
b. 0.787566127 d. 1.612226000
For Problems 71-73:
If money is invested at a nominal rate of interest of 8% for a period of 4 years.
71.) What is the effective rate if it is compounded continuously?
a. 8.33% c. 9.33%
b. 8.93% d. 9.93%
72.) What is the value of the compound amount factor if it is compounded
continuously?
a. 1.377128 c. 1.424231
b. 0.214212 d. 0.122416
73.) What is the value of the present worth factor if it is compounded
continuously?
a. 1. 272441 c. 0.272441
b. 1.726419 d. 0.726149
74.) If the single payment amount factor for a period of 5 years is 1.33822, what is
the nominal rate of interest?
a. 6.00% c. 7.00%
b. 6.92% d.7.92%
75.) What is the effective rate of interest if it is compounded semi-annually of
problem# 74?
a. 5.00% c. 7.24%
b. 6.92% d.6.09%
76.) What is the equivalent nominal rate if it is compounded quarterly of problem#
74?
a. 6.12% c. 4.24%
b. 5.43% d.5.87%
77.) Money was invested at x% compounded quarterly. If it takes money to
quadruple in 17.5 years, find the value of x.
a. 6.23% c. 8.00%
b. 5.92% d.9.78%
78.) What is the actual interest rate of problem# 77?
a. 7.24% c. 7.92%
b. 8.24% d.8.87%
79.) What is the equivalent rate if problem# 77 is compounded daily?
a. 7.24% c. 7.92%
b. 8.24% d.8.87%
For Problems 80-82:
A businessman loaned P500,000 from a local bank that charges an interest rate of
12%.
80.) How much is he going to pay at the end of 5 years if it was made at 12%
simple interest?
a. P800,000.00 c. P911,059.20
b. P823,243.09 d. P907,009.21
compound semi-quarterly?
a. P800,000.00 c. P911,059.20
b. P823,243.09 d. P907,009.21
compound continuously?
a. P800,000.00 c. P911,059.20
b. P823,243.09 d. P907,009.21
83.) P60,000 was deposited at 6% compounded quarterly, tax free for 9 years and 3
months. How much interest was earned at the end of the period?
a. P43,214.24 c. P44,086.60
b. P43.242.24 d. P44,215.60

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84.) P100,000 was placed in a time deposit which earned 9% compounded
quarterly tax free. After how many years would it be able to earn a total interest of
P50,000?
85.) P200,000 was placed in a time deposit at x% compounded quarterly and was
free of taxes. After exactly 5 years, the total interest earned was P120,000. What is
the value of x?
a. 9.5% c. 6.35%
b. 8.21% d. 7.12%
86.) Which of these gives the lowest effective rate of interest?
a. 12.35% compounded annually c. 12.2% compounded quarterly
b. 11.9% compounded semi-annually d. 11.6% compounded
monthly
87.) It takes 20.15 years to quadruple your money if it is invested at x%
compounded semi-annually. Find the value of x.
a. 8% c. 7%
b. 6% d. 5%
88.) It takes 13.87 years to treble the money at the rate of x% compounded
quarterly. Compute the value of x.
a. 5% c. 7%
b. 6% d. 8%
89.) Money was invested at x% compounded quarterly. If it takes the money into
quadruple in 17.5 years, find the value of x.
a. 8% c. 7%
b. 6% d. 5%
90.) Fifteen years ago P1,000.00 was deposited in a bank account, and today it is
worth P2.370.00. The bank pays interest semi-annually. What was the interest rate
paid on this account?
a. 4.9% c. 5.0%
b. 5.8% d. 3.8%
91.) You borrow P3,500.00 for one year from a friend at an interest rate of 1.5%
per month instead of taking a loan from a bank at a rate of 18% per year. Compare
how much money you will save or lose on the transaction.
a. pay P155 more if you borrowed from the bank
b. save P55 by borrowing from your friend
c. pay P85 more if you borrowed from the bank
b. save P95 by borrowing from your friend
92.) Find the present worth of a future payment of P1000,000 to be made in 10
years with an interest of 12% compounded quarterly.
a. P30,444.44 c. P30,655.68
b. P33,000.00 d. P30,546.01
93.) An initial savings deposit of P80,000 in a certain bank earns 6% interest per
annum compounded monthly. If the earnings from the deposit are subject to a 20%
tax, what would the net value of the deposit be after three quarters?
a. P95,324.95 c. P68743.24
b. P82938.28 d. P56244.75
94.) The effective rate of interest of 14% compounded semi-annually is:
a. 14.49% c. 14.94%
b. 14.36% d. 14.88%
95.) The amount of P50,000 was deposited in a bank earning an interest of 7.5%
per annum. Determine the total amount at the end of 5 years, if the principal and
interest were not withdrawn during the period.
a. P71,781.47 c. P70,374.90
b. P72,475.23 d. P78,536.34
96.) What is the effective rate corresponding to 18% compounded daily? Take 1
year is equal to 360 days.
a. 18.35% c. 18.10%
b. 19.39% d. 19.72%
97.) If P1,000 becomes P1,126.49 after 4 years when invested at a certain nominal
rate of interest compounded semi-annually, determine the nominal rate and the
corresponding effective rate.
a. 3.00% and 3.02% c. 2.30% and 2.76%
b. 4.29% and 4.32% d. 3.97% and 3.95%
98.) Convert 12% semi-annually to compounded quarterly.

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a. 19.23% c. 14.67%
b. 23.56% d. 11.83%
99.) What is the corresponding effective interest rate of 18% compounded semi-
quarterly?
a. 19.25% c. 18.46%
b. 19.48% d. 18.95%
100.) If P5000 shall accumulate for 10 years at 8% compounded quarterly, find the
compounded interest at the end of 10 years.
a. P6,005.30 c. P6,040.20
b. P6,000.00 d. P6,010.20
101.) A couple borrowed P4,000 from a lending company for 6 years at 12%. At
the end of 6 years, it renews the loan for the amount due plus P4,000 more for 3
years at 12%. What is the lump sum due?
a. P14,842.40 c. P12,316.40
b. P16,712.03 d. P15,382.60
102.) How long (in years) will it take the money to quadruple if it earns 7%
compounded semi-annually?
103.) P200,000 was deposited on Jan. 1,1988 at an interest rate of 24%
compounded semi-annually. How much would the sum be on Jan. 1, 1993?
a. P421,170 c. P401,170
b. P521,170 d. P621,170
104.) If P500,000 is deposited at a rate of 11.25% compounded monthly,
determine the compounded interest after 7 years and 9 months.
a. P690,849 c. P680,686
b. P670,258 d. P660,592
105.) P200,000 was deposited at an interest rate of 24% compounded semi-
annually. After how many years will the sum be P621,170?
106.) A bank is advertising 9.5% accounts that yields 9.84% annually. How often
is the interest compounded?
a. monthly c. quarterly
b. bi-monthly d. daily
107.) A marketing company established a program to replace the cars of its sales
representatives at the end of every 5 years. If the present price of the approved
type of car is P520,000.00 with a resale value at the end of 5 years of 60% its
present value, how much money must the company accumulate for 5 years if
inflation annually is 10%. Release value will also appreciate at 10% yearly.
a. P120,289.51 c. P110,297.27
b. P129,382.38 d. P122,265.69
108.) In year zero, you invest P10,000.00 in a 15% security for 5 years. During
that time, the average annual inflation is 6%. How much, in terms of year zero will
be in the account at maturity?
a. P15,386.00 c. P13,382.00
b. P15,030.00 d. P16,653.00
109.) A machine has been purchased and installed at a total cost of P18,000.00.
The machine will be retired at the end of 5 years, at which time it is expected to
have a scrap value of P2,000.00 based on current prices. The machine will then be
replaced with an exact duplicate. The company plans to establish a reserve fund to
accumulate the capital needed to replace the machine. If an average annual rate of
inflation of 3% is anticipated, how much capital must be accumulated?
a. P15,030.00 c. P12,382.00
b. P18,548.39 d. P15,386.00
110.) If the inflation rate is 6%, cost of money is 10%, what interest rate will take
care of inflation and the cost of money?
a. 16.6% c. 17.7%
b. 15.5% d. 14.4%
111.) A man bought a government bond which cost P1000 and will pay P50
interest each year for 20 years. The bond will mature at the end of 20 years and he
will receive the original P1000. If there is 2% annual inflation during this period,
what rate of return will the investor receive after considering the effect of
inflation?
a. 2.94% c. 4.25%
b. 3.16% d. 5.16%
112.) The inflated present worth of P2000 in two years is equal to P1471.07. What
is the rate of inflation if the interest rate is equal to 10%?

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a. 6% c. 7%
b. 5% d. 4%
113.) 12% rate of interest can take care of the cost of money and inflation. If the
nominal rate of interest is 6%, what is the rate of inflation?
a. 6.62% c. 7.67%
b. 5.66% d. 4.64%
114.) An engineer bought an equipment for P500,000. Other expenses including
installations amounted to P30,000. At the end of its estimated useful life of 10
years, the salvage value will be 10% of the first cost. Using straight line method of
depreciation, what is the book value after 5 years?
a. P291,500 c. P242,241
b. P282,242 d. P214,242
115.) A small machine costing P80,000 has a salvage value of x at the end of its
life of 5 years. The book value at the end of the 4th
year is P22,400. What is the
value of x using the straight line method depreciation?
a. P6000 c. P8000
b. P7000 d. P9000
116.) A machine has a salvage value of P12,000 at the end of its useful life of 6
years. The book value at the end of 5 years is P30,833.33. Using a straight line
method of depreciation, what is the first cost of the machine?
a. P125,500 c. P125,000
b. P135,500 d. P135,000
117.) A manufacturing plant was built at a cost of P5M and is estimated to have a
life of 20 years with a salvage value of P1M. A certain equipment worth P570,000
was installed at a cost of P80,000 is expected to operate economically for 15 years
with a salvage value of P50,000. Determine the book value of the plant and
equipment after 10 years, use straight line depreciation method.
a. P3,250,000 c. P4,250,000
b. P3,750,000 d. P4,500,000
118.) A printing equipment costs P73,500 has a life expectancy of 8 years and has
a salvage value of P3,500 at the end of its life. The book value at the end of x years
is equal to P38,500. Using straight line method of depreciation, solve for the value
of x.
119.) The cost of the printing equipment is P500,000 and the cost of handling and
installation is P30,000. If the book value of the equipment at the end of the 3rd
year
is P242,000 and the life of the equipment is assumed to be 5 years, determine the
salvage value of this equipment at the end of 5 years.
a. P50,000 c. P53,000
b. P60,000 d. P64,000
120.) An engineer bought an equipment for P500,000. He spent an additional
amount of P30,000 for installation and other expenses. The salvage value is 10%
of the first cost. If the book value at the end of 5 years will be P291,500 using
straight line method of depreciation, compute the useful life of the equipment in
years.
121.) The cost of equipment is P500,000 and the cost of installation is P30,000. If
the salvage value is 10% of the cost of equipment at the end of 5 years, determine
the book value at the end of the fourth year. Use straight line method.
a. P155,000 c. P146,000
b. P140,000 d. P132,600
For Problems 122-124:
The first cost of a machine is P1,800,000 with a salvage value of P300,000 at the
end of its life of 5 years. Determine the total depreciation after 3 years.
122.) Using Straight Line Method
a. P800,000 c. P900,000
b. P600,000 d. P700,000
123.) Using Sum of Years Digit Method
a. P1,150,000 c. P1,300,000
b. P1,200,000 d. P1,350,600
124.) Using Constant Percentage Method
a. P1,355,024.24 c. P1,246,422.53
b. P1,185,769.76 d. P1,432,624.84

23
125.) An asset is purchased for P9,000.00. Its estimated economic life is 10 years
after which it will be sold for P1,000.00. Find the depreciation in the first three
years using straight line method.
a. P2,500 c. P3,000
b. P2,400 d. P2,000
126.) The purchase of a motor for P6000 and a generator for P4000 will allow the
company to produce its own energy. The configuration can be assembled for P500.
The service will operate for 1600 hours per year for 10 years. The maintenance
cost is P300 per year, and cost to operate is P0.85 per hour for fuel and related
cost. Using straight line depreciation, what is the annual cost for the operation?
There is a P400 salvage value for the system at the end of 10 year.
a. P2,710 c. P2,630
b. P2,480 d. P2,670
127.) A machine has an initial cost of P50,00.00 and a salvage value of P10,000.00
after 10 years. What is the straight line method depreciation rate as a percentage of
the initial cost?
a. 10% c. 12%
b. 8% d. 9%
128.) A machine has an initial cost of P50,00.00 and a salvage value of P10,000.00
after 10 years. What is the book value after 5 years using straight line method
depreciation rate?
a. P35,000 c. P15,500
b. P25,000 d. P30,000
129.) A machine has a first of P80,000 and a salvage of P2,000 at the end of its life
of 10 years. Find the book value at the end of the 6th
year using straight line
method of depreciation.
a. P33,200 c. P34,300
b. P35,400 d. P32,900
130.) An asset is purchased for P90,000.00. Its estimated life is 10 years after
which it will be sold for P1,000.00. Find the book value during the first year if
Sum of the Years Digits(SYD) depreciation is used.
a. P7,545.45 c. P5,245.92
b. P2,980.24 d. P6,259.98
131.) A telephone company purchased a microwave radio equipment for P6M.
Freight and installation charges amounted to 3% of the purchased price. If the
equipment shall be depreciated over a period of 8 years with a salvage value of
5%, determine the depreciation charge during the 5th
year using the Sum of Year
Digit Method.
a. P756,632.78 c. P652,333.33
b. P957,902.56 d. P845,
935.76
132.) A consortium of international communications companies contracted for the
purchase and installation of a fiber optic cable linking two major Asian cities at a
total cost of P960M. This amount includes freight and installation charges at 10%
of the above total contract price. If the cable depreciated over a period of 15 years
with zero salvage value, what is the depreciation charge during the 8th
year using
the sum of year digits method?
a. P64M c. P80M
b. P23M d. P76M
133.) A machine cost P7,350 has a life of 8 years and has a salvage value of P350
at the end of 8 years. Determine its book value at the end of 4 years using sum
years digit method.
a. P3,476.90 c. P6,543.21
b. P2,294.44 d. P5,455.01
134.) A certain equipment costs P7,000 has an economic life of n years and a
salvage value P350 at the end of n years. If the book value at the end of 4 years is
equal to P2197.22, compute for the economic life of the equipment using the sum
of years digit method.
135.) A company purchased an asset for P10000 and plans to keep it for 20 years.
If the salvage value is zero at the end of the 20th
year, what is the depreciation in
the third year? Use sum of years digit method.
a. P1000 c. P938
b. P857 d. P747
136.) An equipment costs P7000 and has a life of 8 years and salvage value of x
after 8 years. If the book value of the equipment at the 4th
year is equal to
P2197.22, compute the salvage value x using the sum of years digit method.
a. P594 c. P350
b. P430 d. P290
137.) ABC Corporation makes it policy that for every new equipment purchased,
the annual depreciation should not exceed 20% of the first cost at any time without

23
salvage value. Determine the length of service if the depreciation used is the SYD
Method.
138.) A machine having a certain first cost has a life of 10 years and a salvage
value of 6.633% of the first cost at the end of 10 years. If it has a book value of
P58,914 at the end of the 6th
year, how much is the first cost of the machine if the
constant percentage of declining value is used in the computation for its
depreciation.(Matheson’s Method)
a. P600,000 c. P100,000
b. P300,000 d. P900,000
139.) A machine costing P720,000 is estimated to have a life of 10 years. If the
annual rate of depreciation is 25%, determine the total depreciation using a
constant percentage of the declining balance method.
a. P679,454.27 c. P532,825.73
b. P432,725.45 d. P764,243.33
140.) An earth moving equipment that cost P90,000 will have an estimated salvage
value of P18,000 at the end of 8 years. Using double-declining balance method,
compute the book value and the total depreciation at the end of the 5th
year.
a. P21,357.42 ; P68,642.58 c. P24,362.48 ;
P65,637.52
b. P15,830.34 ; P74,169.66 d. P19,442.78 ;
P70,557.22
141.) A certain office equipment has a first cost of P20,000 and has a salvage value
of P1,000 at the end of 10 years. Determine the depreciation at the end of the 6th
year using Sinking fund method at 3% interest.
a. P10,720 c. P11,680
b. P12,420 d. P9,840
142.) An equipment which cost P200,000 has a useful life of 8 years with a
salvage value of P25,000 at the end of its useful life. If the depreciation at the first
year is P21,875, what method is used in the calculation of depreciation?
a. Straight Line c. Declining Balance
b. Sinking Fund d. Sum of Years Digit
143.) An equipment costs P8,000 has an economic life of 8 years and salvage
value of P400 at the end of 8 years. The first year depreciation amounts to
P1,688.89. What method is used in the calculation of the depreciation?
144.) The original cost of a certain machine is P150,000 and has an economic life
of 8 years with a salvage value of P9,000 at that time. If the depreciation of the
first year is equal to P44,475, what method is used in the calculation of the
depreciation?
145.) A machine has a first cost of P140,000 and a life of 8 years with a salvage
value of P10,000 at the end of its useful life. If the depreciation at the first year
amounts to P35,000, what method is used in the calculation of depreciation?
a. Double Declining Balance c.
Straight Line
b. Declining Balance d. Sum of
Years Digit
146.) A hydraulic machine cost P180,000 and has a salvage value of P15,000 at the
end of its useful life which is 12 years. If the depreciation at the first year is
P9,780.71, what method is used in computing the depreciation. Assume money is
worth 6% annually.
147.) An equipment costs P480,000 and has a salvage value of 10% of its cost at
the end of its economic life of 35,000 operating hours. In the first year, it was used
for 4,000 hours. Determine its book value at the end of the first year.
a. P430,629.00 c. P418,360.00
b. P380,420.00 d. P376,420.00
148.) An equipment costs P480,000 and has a salvage value of 10% of its cost at
the end of its economic life of 36,000 operating hours in a period of 5 years. In the
first year of service, it was used for 12,000 hours. If at the end of the 2nd
year it
was used for 15,000 hours, find the depreciation at the second year.
a. P180,000 c. P190,000
b. P160,000 d. P150,000
149.) A certain machine cost P40,000 and has a life of 4 years and a salvage value
of P5000. The production output of this machine in units per year is 1000 units for
the first year, 2000 units for the second year, 3000 units for the third year, and
4000 units for the fourth year. If the units produced are in uniform quality, what is
the depreciation charge at the end of the fourth year.

23
a. P14,000 c. P15,000
b. P13,000 d. P16,000
150.) A lathe machine costs P300,000 brand new with a salvage value of x pesos.
The machine is expected to last for 28500 hours in a period of 5 years. In the first
year of service it was used for 8000 hours. If the book value at the end of the first
year is P220,000, compute for the salvage value x in pesos.
a. P15,000 c. P12,000
b. P18,000 d. P20,000
151.) A certain machine cost P40,000 and has a life of 4 years and a salvage value
of P5000. The production output of this machine in units per year is first year 1800
units, second year2200 units, third year 3000, and fourth year 4000 units. If the
units produced are of uniform quality, what is the depreciation charge at the end of
4th
year?
a. P12,727.27 c. P16,420.43
b. P15,350.23 d. P17,200.98
152.) A lathe machine cost P300,000 with a salvage value of P15,000 is expected
to last for 285000 hours in a period of 5 years. In the first year of service it was
used for 8000 hours. Compute the book value of the machine at the end of the first
year.
a. P292,000 c. P250,000
b. 200,000 d. P323,000
153.) A machine costing P280,000 has a useful life of 20,000 hrs. at the end of
which its salvage value is P30,000. In the first year, it was used for 2080 hrs, in the
second year, 3160 hrs. Find the second depreciation cost in pesos.
a. P23,520 c. P39,500
b. P25,252 d. P35,400
154.) An equipment costs P400,000 and has a life of 30,000 hrs at the end of
which its salvage value is x pesos. In the first year, it was used for 6240 hrs. The
book value at the end of the first year was P325,120. Find the value of x.
a. P40,629 c. P40,000
b. P30,420 d. P30,000
155.) An engineering firm from purchased, 12 years ago, a heavy planner for
P50,000 with no salvage value. As the life of the planner was 20 years, a straight
line depreciation reserve has been provided on that basis. Now the firm wishes to
replace the old planner with a new one possessing several advantages. It can sell
the old planner for P10,000. The new one will cost P100,000. How much new
capital will be required to make the purchase?
a. P60,000 c. P66,000
b. P55,000 d. P57,000
156.) Ten years ago, a contractor was able to purchase a crane whose capacity is
2000 tons costing P125 per ton. The life was estimated to be 15 years with a
salvage value of 10% of the cost. A market has been found for the old crane for
P80,000. If the depreciation has been figured on a straight line basis what is the
difference between the depreciation book value of the old crane and its sale value.
a. P20,000 c. P15,000
b. P30,000 d. P10,000
157.) What is the nominal value of interest compounded continuously for a period
of 5 years of an equal payment series if the capital recovery factor is equal to
0.2385787.
a. 6% c. 5%
b. 4% d. 8%
158.) What is the nominal rate of interest compounded continuously for a period of
5 years of an equal payment series if the sinking fund factor is equal 0.180519?
a. 5% c. 6%
b. 4% d. 8%
159.) Compute the number of years so that the capital recovery factor of a uniform
payment series be equal to 0.218638 if money is worth 3% compounded
continuously.
a. 5 c. 6
b. 4 d. 3
160.) A manufacturing firm wishes to give each 80 employee a holiday bonus.
How much is needed to invest monthly for a year at 12% nominal interest rate,
compounded monthly, so that each employee will receive a P2000 bonus?
a. P12,608 c. P12,600
b. P12,615 d. P12,300
161.) An instructor plans to retire in one year and want an account that will pay
him P25000 a year for the next 15 years. Assuming 6% annual effective interest
rate, what is the amount he would need to deposit now? (The fund will be depleted
after 15 years)
a. P249,000 c. P248,500
b. P242,806 d. P250,400

23
162.) Ryan invest P5,000 at the end of each year in an account which gives a
nominal annual interest of 7.5%, compounded continuously. Determine the total
worth of his investment at the end of 15 years.
a. P133,545.58 c. P126,336.42
b. P142,647.28 d. P135,429.64
163.) A car dealer advertise the sale of a car model far a cash price of P280,000. If
purchased in installment, the required down payment is 15% and balance payable
in 18 equal monthly installments at an interest rate of 1.5% per month. How much
will be the required monthly payments?
a. P15,185.78 c. P10,972.33
b. P11,588.72 d. P15,558.12
164.) How much must be deposited at 6% each year beginning Jan 1, year 1, in
order to accumulate P5,000 on the date of the last deposit, Jan 1, year 6?
a. P751 c. P715
b. P717 d. P775
165.) In anticipation of a much bigger volume of business after 10 years, a
fabrication company purchased an adjacent lot for its expansion program where it
hopes to put up a building projected to cost P4,000,000 when it will be constructed
10 years after. To provide for the required capital expense, it plans to put up a
sinking fund for the purpose. How much must the company deposit each year if
the interest to be earned is computed at 15%
a. P197,008.25 c. P177,009.25
b. P199,090.25 d. P179,008.25
166.) Rainer Wandrew borrowed P50,000 from Social Security System, in the
form of calamity loan, with interest at 8% quarterly installments for 10 years. Find
the quarterly payments.
a. P1827.79 c. P1287.78
b. P1892.18 d. P1972.36
167.) For having been loyal, trustworthy, and efficient, the company has offered a
superior yearly gratuity pay of P20,000 for 10 years with the first payment to be
made one year after his retirement. The supervisor, instead, requested that he be
paid a lump sum, on the date of his retirement, having less interest that the
company would have earned if the gratuity is to be paid in yearly basis. If interest
is 15%, what is the equivalent lump sum that he could get?
a. P100,375.37 c. P101,757.37
b. P100,735.37 d. P100,575.37
168.) If P500 is invested at the end of each year for 6 years, at an annual interest
rate of 7%, what is the total peso amount available upon the deposit of the sixth
payment?
a. P3,210 c. P3,000
b. P3,577 d. P4,260
169.) A series of year and payments extending over eight years are as follows:
P10,000 for the first year, P20,000 for the second year, P50,000 for the third year,
and P40,000 for each year from fourth year through the 8th
year. Find the
equivalent annual worth of these payments if the annual interest is 8%.
a. P44,800.00 c. P35,650.00
b. P30,563.00 d. P33,563.85
170.) In five years, P18,000 will be needed to pay for a building renovation,. In
order to generate this sum, a sinking fund consisting of three annual payments is
established now. For tax purposes, no further payments will be made after three
years. What payments are necessary if money is worth 15% per annum?
a. P2870 c. P5100
b. P3919 d. P2670
171.) San Miguel Corporation purchases P400,00 worth of equipment in year
1970. It decided to use straight line depreciation over the expected 20 year life of
the equipment. The interest rate is 16%. If the overall tax rate is 35% , what is the
present worth of the tax shield?
a. P40,298.68 c. P45,450.28
b. P41,501.89 d. P51,410.37
172.) A local firm is establishing a sinking fund for the purpose of accumulating a
sufficient capital to retire its outstanding bonds and maturity. The bonds are
redeemable in 10 years, and their maturity value is P150,000. How much should
be deposited each year if the fund pays interest at the rate of 3%?
a. P12,547.14 c. P14,094.85
b. P13,084.58 d. P16,848.87
173.) A machine costs P20,000 today and has an estimated scrap value of P2,000
after 8 years. Inflation is 2% per year. The effective annual interest rate earned on
money invested is 8%. How much money needs to be set aside each year to
replace the machine with an identical model 8 years from now?
a. P2,808.88 c. P3,920.00
b. P3,290.00 d. P3,610.00
174.) A machine is under consideration for investment. The cost of the machine is
P25,000. Each year it operates, the machine generates P15,000. Given an effective
annual interest rate of 18%, what is the discounted payback period, in years, on the
investment of the machine?

23
175.) Company A purchases P200,000 of equipment in year zero. It decides to use
straight line depreciation over the expected 20 year life of the equipment. The
interest rate is 14%. If the average tax rate is 40%, what is the present worth of the
depreciation tax held?
a. P30,500 c. P39,700
b. P26,500 d. P40,000
176.) Instead of paying P100,000 in annual rest for office space at the beginning of
each year for the next 10 years, an engineering firm has decided to take out a 10
year P100,000 loan for a new building at 6% interest. The firm will invest
P100,000 of the rent saved and earned 18% annual interest on that amount. What
will be the difference between the revenue and expenses?
a. Firm will need P17,900 extra c. Firm will have P21,500 left over
b. Firm will break even d. Firm will need P13,000
extra
177.) A man inherited a regular endowment of P100,000 every end of 3 months for
x years. However, he may choose to get a single lump of P3,702,939,80 at the end
of 4 years. If the rate interest was 14% compounded quarterly, what is the value of
x?
b. 10 years d. 11 year
178.) A service car whose car price was P540,000 was bought with a down
payment of P162,000 and monthly installments of P10,847.29 for 5 years. What
was the rate of interest if compounded monthly?
a. 30% c. 20%
b. 24% d. 15%
179.) What is the present worth of a 3 year annuity paying P3000 at the end of
each year, with interest at 8% compounded annually?
a. P7,731.29 c. P7,371.29
b. P9,731.79 d. P9,371.79
180.) A man paid a 10% down payment of P200,000 for a house and lot and agreed
to pay the balance on monthly installments for 5 years at an interest rate of 15%
compounded monthly. What was the monthly installment on pesos?
a. P44,528.34 c. P43,625.92
b. P42,821.87 d. P45,825.62
181.) A man inherited a regular endowment of P100,000 every end of 3 months for
10 years. However, he may choose to get a single lump sum payment at the end of
4 years. How much is this lump sum if the cost of money is 14% compounded
quarterly?
a. P3,702,939.73 c. P3,502,546.23
b. P3,802,862.23 d. P3,602,431.73
182.) A man paid 10% down payment of P200,000 for a house and lot and agreed
to pay the balance on monthly installments for x years at an interest rate of 15%
compounded monthly. If the monthly installment was P42,821.87, find the value of
x.
a. 5 years c. 8years
b 9 years d. 7 years
183.) A father wishes to provide P4000 for his son on his 21st
birthday. How much
should he deposit every 6 months in a savings bank which pays 3% compounded
semi-annually if the first deposit is made when the son is 3.5 years old?
a. P84.61 c. P45.76
b. P94.24 d. P78.68
184.) An employee obtained a loan of P100,000 at the rate of 6% compounded in
order to build a house. How much must he pay monthly to amortize the loan
within a period of 10 years?
a. P8,322.07 c. P2,494.04
b. P1,101.80 d. P3,452.90
185.) If money is worth 5% compounded semi-annually, find the present value of a
sequence of 12 semi-annual payments of P500 each, the first of which is due at the
end of 4.5 years.
a. P4,209.51 c. P6,240.62
b. P5,602.62 d. P7,161.42
186.) An annual deposit of P1270 is placed on the fund at the end of each year for
6 years. If the fund invested has a rate of interest of 5% compounded annually,
how much is the worth of this fund at the end of 9 years?
a. P12,000 c. P11,000
b. P10,000 d. P14,000
187.) A fund for replacement of a machinery in a plant must have P30,000 at the
end of 9 years. An equal deposit of P2,965 was made on the fund at the end of

23
each 6 months for 4 years only. How much is the rate of the fund invested if it is
compounded semi-annually?
a. 3.5% c. 5.5%
b. 4.5% d. P6.5%
188.) In purchasing a house, a man makes a cash payment and takes out a
mortgage for P10,000 on which he agrees to pay P200 at the end of each month for
5 years. At what interest rate compounded monthly was interest charged on the
mortgage?
a. 8.41% c. 7.68%
b. 7.42% d. 9.60%
189.) How much money must you invest in order to withdraw P2000 annually for
10 years if the interest rate is 9%?
a. P12,853.32 c. P12,835.32
b. P12,881.37 d. P12,385.32
190.) If interest is at rate of 8% compounded semi-annually, what sum must be
invested at the end of each 6 months to accumulate a fund of P10,000 at the end of
8 years?
a. P458.20 c. P498.23
b. P532.11 d. P753.10
191.) A Corporation will invest P5000 in a fund at the end of each 6 months to
accumulate P100,000 to initiate a plant overhaul. If the fund is invested at 6.5%
compounded semi-annually, how may years will the fund contain at least
P100,000?
192.) A piece of machinery can be bought for P10,000 cash, or for P2000 down
and payments of P750 per year for 15 years. What is the annual interest rate for
time payments?
a. 4.61% c. 5.71%
b. 3.81% d. 11.00%
193.) To accumulate a fund of P8000 at end of 10 years, a man will make equal
annual deposit of P606.94 in the fund at the end of each year. How much is the rate
of interest if it is compounded annually?
a. 6% c. 10%
b. 8% d. 12%
194.) A purchasing engineer of a certain firm is to purchase a second hand truck
fro P75,000. A dealer offers cash payment of P5,000 and P6486 per month for 12
months. Another dealer offered under the same condition with 0.75% interest per
month for 12 months of the unpaid balance. Which offer should the engineer
choose and what is the rate of interest?
a. 0.62% c. 0.75%
b. 1.66% d. 0.40%
195.) If a low cost house and lot worth P87,000 were offered at 10% down
payment and P500 per month for 25 years. What is the effective monthly interest
rate on the diminished balance?
a. 0.492% c. 0.531%
b. 0.687% d. 0.683%
196.) A house and lot can be acquired with a down payment of P500,000 and a
yearly payment P100,000 at the end of each year for a period of 10 years, starting
at the end of 5 years from the date of purchase. If the money is worth 14%
compounded semi-annually, what is the cash price of the property?
a. P810,000 c. P801,900
b. P808,836 d. P805,902
197.) A man bought a brand new car for P650,000 on installment basis at the rate
of 10% oer annum on the unpaid balance. If he paid a down payment of P120,000
cash and proposed to pay the balance in equal monthly payment for 2 years, what
should be his monthly payment?
a. P54,323.03 c. P24,447.03
b. P34,532.94 d. P83,534.32
198.) A businessman is faced with the prospect of fluctuating future budget for the
maintenance of the generator. During the first 5 years, P1,000 per year will be
budgeted. During the second 5 years, the annual budget will be P1500 per year. In
addition, P3500 will be budgeted for an overhaul of the machine at the end of the
fourth year and another P3500 for an overhaul at the end of 8th
year. Assuming
compounded interest at 6% per annum, what is the equivalent annual cost of
maintenance?
a. P1,888.87 c. P1,777.38
b. P1,738.34 d. P1,999.34
199.) A parent on the day the child is born wishes to have to determine what lump
sum would have to be paid into an account bearing interest at 5% compounded
annually, in order to withdraw P20,000 each on the child’s 18th
, 19th
, 20th
, and 21st
birthdays.
a. P35,941.73 c. P30,941.73

23
b. P33,941.73 d. P25,941.73
200.) If money is worth 5% compounded semi-annually, find the present value of a
sequence of 12 semi-annual payments of P500 each, the first of which is due at the
end of 4.5 years.
a. P4,209.51 c. P3,958.48
b. P5,038.29 d. P4,936.39
201.) A businessman borrowed P300,000 with interest at the rate of 6%
compounded semi-annually. He agrees to discharge his obligation by paying a
series of 8 equal semi-annual payments, the first being due at the end of 5.5 years.
Find the semi-annual payment.
a. P69,475.53 c. P73.083.59
b. P57,434.78 d. P40,922.40
202.) A man borrowed P300,000 from a lending institution which will be paid after
10 years at an interest rate of 12% compounded annually. How much should he
deposit to a bank monthly in order to discharge his debt 10 years hence?
a. P2,798.52 c. P4,672.31
b. P3,952.50 d. P5,093.06
203.) What is the accumulated amount of the five year annuity paying P6000 at the
end of each year, with interest at 15% compounded annually?
a. P40,454.29 c. P41,454.29
b. P41,114.29 d. P40,544.29
204.) A man owes P12,000 today and agrees to discharge the debt by equal
payments at the beginning of each 3 months for 8 years, where this payments
include all interest at 8% payable quarterly. Find the quarterly payment.
a. P501.30 c. P498.20
b. P602.40 d. P701.60
205.) A man will deposit P200 with a savings and loan association at the beginning
of 3 months for 9 years. If the association pays interest at the rate of
5.5%quarterly, find the sum to his credit just after the last deposit.
a. P9236 c. P9563
b. P9363 d. P9684
206.) At what interest rate payable quarterly will payments of P500 at the
beginning of each 3 months for 7 years discharge a debt of P12500 due
immediately?
a. 3.44% c. 5.44%
b. 4.33% d. 6.33%
207.) A P1,000,000 issue of 3% 15 years bonds was sold at 95%. If miscellaneous
initial expences of the financing were P20,000 and yearly expenses of P2,000 is
incurred, what is the true cost the company is paying for the money it borrowed?
a. 3.8% c. 4.0%
b. 4.2% d. 2.6%
208.) A man was offered a Land Bank certificate with a face value of P100,000
which is baring interest of 8% per year payable semi-annually and due in 6 years.
If he wants to earn 6% semi-annually, how much must he pay the certificate?
a. P90,614.92 c. P90,061.49
b. P96,041.92 d. P99,814.92
209.) The National Irrigation Administration undertakes the construction of an
irrigation project in the province of oriental Mindoro which will cover an area of
10,000 hectares and estimated cost P10,000,000 which was borrowed from the
World Bank at the start of the construction. The construction will last 30 years
with no salvage value. Bonds will be paid at 4% per annum compounded annually
for 30 years. The construction of project will take 4 years. Insurance operation and
maintenance of the system will cost P120,00 per year. Interest on sinking fund is
6%. How much should each hectare be charged?
a. P64.65 c. P60.66
b. P66.56 d. P45.65
210.) A company issued 50 bonds of P1,000 face value each redeemable at par at
the end of 15 years to accumulate the funds required fro redemption. The firm
established a sinking fund consisting of annual deposits, the interest rate of the
fund being 4%. What was the principal in the fund at the end of 12th
year?
a. P35,983 c. P41,453
b. P38,378 d. P37,519
211.) An oil well which could produce a net income of P15,000,000 per year for 25
years is being considered to be purchased by a group of businessman. If the return
on investment is targeted to be 20% out of the net income and the sinking fund at
18% interest is to be established at recover of investment, how much must be paid
to the oil well?
a. P73,921,184.58 c.
P70,215,276.17
b. P73,297,198.28 d.
P75,973,209.26

23
212.) An investor pays P1,100,000 for a mine which will yield a net income of
P200,000 at the end of each year for 10 years and then will become useless. He
accumulated a replacement fund to recover his capital by annual investments at
4.5%. At what rate(%) does he receive interest on his investment at the end of each
year?
a. 10.04% c. 11.5%
b. 8.5% d. 14.5%
213.) A certain marble mine property has an estimated life of 30 years at a
projected annual output of 3000 cubic meters of marble blocks. Estimated
management cost per year is placed at P1,500,000 and operating cost of the quarry
and processing plant is P8000 per cubic meter. The finished products, tiles and
slabs, can be sold for P12,000 per cubic meter if exported. Determine the present
valuation of the mineral property if the sinking fund rate of interest is 15% and the
annual dividend rate is to be 12%.
a. P85,854,317.13 c.
P85,444,313.27
b. P85,554,371.18 d.
P85,345,365.28
214.) The annual dividend from a mine will be P75,000 until the ore is exhausted
at the end of 30 days, and the mine becomes useless. Find the price of the mine to
yield the investor 6.5%, if he accumulated a replacement fund to restore his capital
by annual investment at 5%.
a. P936,897.63 c. P982,286.29
b. P836,286.39 d. P735,385.53
215.) The privileges of a patent will last for 20 more years and the royalty from it
will be P60,000 at the end of each year during that time. Find the value of his
patent rights to an investor who desires interest at 8% on his investment and will
accumulate a capital replacement fund at 5%.
a. P594,297.20 c. P405,384.28
b. P544,254.30 d. P629,289.40
216.) The annual income from the mine is P100,000 and the life of the mine is 20
years. Find the price that an investor is willing to pay for the mine if he considers
that money is worth 5% and if he is to accumulate a sinking fund at 6% in order to
replace the capital he invested.
a. P1,295,595.57 c.
P1,529,847.29
b. P1,995,959.97 d.
P1,159,287.92
217.) An untreated electric wooden pole that will last 10 years under a certain soil
conditions costs P1200. If a treated pole will last for 20 years, what is the
maximum justifiable amount that can be paid for the treated pole, if the maximum
return on investment is 12%? Consider annual taxes and insurance amount to be
1% at first cost.
a. P1,559.50 c. P1,593.20
b. P1995.28 d. P1,959.30
218.) A company must relocate one of its factories in three years. Equipment for
the loading dock is being considered for purchase. The original cost is
P20,000,000, the salvage value of the equipment after three years is P8,000. The
company’s rate of return on money is 10%. Determine the capital recovery rate per
year.
a. P5115 c. P5625
b. P4946 d. P4805
219.) A new engine will cost P12,000 with an estimated life of 15 years and a
salvage value of P800 and guaranteed to have an operating cost of P3500 per year.
The new engine is considered as a replacement of the old one. The old engine had
a total annual cost of P5,200 to operate. Determine the rate of return of the new
investment using 6% sinking fund to recover depreciation, if the old engine could
be sold now for P2000.
a. 12.19% c. 10.47%
b. 14.29% d. 15.92%
220.) A corporation uses a type of motor truck which costs P5000with a life of 2
years and final salvage value of P800. How much could the corporation afford to
pay for another type of truck of the same purpose for a life of 3 years with a final
salvage value of P1000? Money is worth 4%
a. P8450.66 c. P6398.24
b. P7164.37 d. P9034.56
221.) A granite quarry purchased of P1,600,000 is expected to be exhausted at the
end of 4 years. If the resale value of the land is P100,000, what annual income is
required to yield an investment rate of 12%? Use a sinking fund rate of 3%
a. P551,544 c. P550,540
b. P552,550 d. P553,420
222.) A machine has a first cost of P800,000 and a salvage value of P50,000 at the
end of its life after 10 years. The annual saving for the use of the machine amount
s to P124,900.97. If the annual maintenance of the machine is P4000 and the
sinking fund to recover depreciation earns 6%, compute for the rate of return of
investment.
a. 8% c. 6%
b. 7% d. 9%

23
223.) The first cost of a certain equipment is P324,000 and a salvage value of
P50,000 at the end of its life of 4 years. If money is worth 6% compounded
annually, find the capitalized cost.
a. P1,367,901.15 c. P936,431.16
b. P1,427,846.17 d. P843,916.27
224.) A multi million project can purchase heavy duty trucks for P600,000 each. It
is estimated to have a salvage value of P60000 at the end of its life which is 10
years. Maintenance and operating cost including the driver is estimated to cost an
average of P3000 per year. The contractor however can hire a similar truck and its
operator for P420 per day. If money is worth 12%, how many days per year must
the service of the truck be required to justify the buying of the trucks. Use annual
cost method.
a. 252 days c. 243 days
b. 225 days d. 255 days
225.) Each removal from a ditch in city streets is accomplished by a machine
loading into trucks. This machine will cost P20,000 with labor, fuel, oil, and
maintenance amounting to P5000 per year. Life of the machine is estimated to be 5
years and no salvage value. The contractor however can hire a similar machine and
its operator at P340 per day. How many days per year must the services of the
machine be required to justify the purchase of their new machine of the money is
worth 10%. Use annual cost method.
226.) A contractor can purchase a heavy-duty truck for P500,000. Its estimated life
is 8 years and estimated salvage value of P6000. Maintenance is estimated to be
P2500 annually including the cost of driver and fuel maintenance. The contractor
can hire a similar unit and driver for P750 a day. If interest is taken at 8%, how
many days per year must be services of a dump truck be required to justify the
purchase of a truck? Use annual cost method.
b. 121days d. 211 days
227.) It cost P50,000 at the end of each year to maintain a section of Kennon road.
If money is worth 10%, how much would it pay to spend immediately to reduce
the annual cost to P10,000?
a. P410,000 c. P400,000
b. P554,000 d. P453,000
228.) If money is worth 12% compounded quarterly, what is the present value of
the perpetuity of P1,000 payable monthly?
a. P453,876.80 c. P342,993.70
b. P100,976.23 d. P100,993.78
229.) Find the present value, in peso, of a perpetuity of P15,000 payable semi-
annually if money is worth 8% compounded quarterly.
a. P372,537 c. P373,767
b. P374,977 d. P371,287
230.) A businessman invested in a medium scale business which cost him P47,000.
The net annual return estimated is P14,000 for each of the next 8 years. Compute
the benefit cost ratio if the annual rate of interest is 18%.
a. 1.21 c. 2.23
b. 1.76 d. 1.11
231.) A project costs P100,000. The benefit at the end of each year for a period of
5 years is equal to P40,000. Assuming money is worth 8% with no salvage value,
compute the benefit cost ratio.
a. 1.597 c. 1.875
b. 2.124 d. 1.125
232.) Compute the benefit cost ratio of the following project:
Project cost = P80,000
Gross income = P25,000 per year
Opening Cost = P6,000 per year
Salvage Value = 0
Life of Project = 10 years
Rate of Interest = 12%
a. 1.34 c. 2.23
b. 1.78 d. 1.11
233.) A local factory assembling calculators produces 100 units per month and
sells them at P1,800 each. Dividends are 8% on the 8000 shares with par value of
P250 each. The fixed operating cost per month is P25,000. Other costs are P1,000
per unit. Determine the break even point. If only 200 units were produced per
month, determine the profit.
a. 48 ; P121,666.67 c. 50 ;
P112,656.67
b. 45 ; P122,676.88 d. 48 ;
P212,666.67
234.) General Electric Company, which manufactures electric motor, has a
capacity of producing 150 motors a month. The variable costs are P4,000 per
month, the average selling price of the motor is P750 per motor. Fixed costs of the
company amounts to P78,000 per month which includes all taxes. Determine the
number of motors to be produced per month to break even and the sales volume in
pesos at this point.
a. 110 units c. 105 units

23
b. 120 units d. 115 units
235.) A plywood manufacturer produces a piece of plywood at a labor cost of
P0.50 and material at P3.00. The fixed charges on business are P50,000 a month
and the variable cost is P0.50 per piece. If one plywood sells for P6.00 each, how
many pieces must be produced each month for the manufacturer to break even?
a. 25,000 c. 24,000
b. 27,000 d. 22,000
236.) The profit on a product selling for P8.20 is 10% of the selling price. What
percentage increase in production cost will reduce the profit by 60%?
a. 6.67% c. 7.66%
b. 6.76% d. 7.66%
237.) A local company assembling stereo radio cassette produces 300 units per
month at a cost of P800 per unit. Each stereo radio cassette sells for P1,200. If the
firm makes a profit of 10% on its 10,000 shares with a par value of P200 per share,
and the total fixed cost is P20,000 per month. What is the break even point and
how much is the loss or profit if only 100 units are produced in a given month?
a. 92 ; P3,333.33 c. 91 ; P4,333.44
b. 90 ; P3,444.33 d. 93 ; P4,444.33
238.) A certain operation is now performed by hand, the labor cost per unit is
P0.54 and the annual fixed charge for tool used is estimated at P100 per year. A
machine that is being considered for this job will cost P2,400, have a salvage value
of P100 at any time and a fixed annual cost of P200. With it, labor cost is P0.22
per unit. For what number of units of product per year at zero interest and life of 6
years for the machine will the annual cost of the two methods break even?
239.) A shoe manufacturer produces a pair of shoes at a labor cost of P9.00 a pair
and a material cost of P8.00 a pair. The fixed charges on the business is P90,000 a
month and the variable cost is P4.00 a pair. If the shoes sells at P30 a pair, how
many pairs must be produced each month for the manufacturer to break even?
a. 10,000 c. 11,000
b. 12,000 d. 13,000
240.) An item which can be sold for P36.00 per unit wholesale is being produced
with the following cost data; labor cost, P10 per unit; material cost, P15.00 per
unit; fixed charges, P10,000; variable cost, P8.00 per unit. What is the break even
point sales volume and the break even sales volume if one out of every ten units
produced is defective and is rejected with only full recovery on materials?
a. 333.33 ; 397 c. 353.33 ; 333
b. 345.33 ; 379 d. 322.33 ; 377
241.) A certain firm has the capacity to produce 650,000 units of product per year.
At present, it is operating at 62% capacity. The firm’s annual income is
P4,160,000. Annual fixed cost is P1,920,000 and the variable cost is equal to P3.56
per unit of product. What is the firm’s annual profit or loss and what volume of
sales does the firm break even?
a. P805,320 ; P3,354,680 c. P803,550 ; P3,276,398
b. P850,330 ; P3,543,683 d. P800,286 ; P3,186,586
242.) The direct labor cost and material cost of a certain product are P300 and
P400 per unit, respectively. Fixed charges are P100,000 per month and other
variable costs are P100 per unit. If the product is sold at P1,200 per unit, how
many units must be produced and sold to break even?
243.) XYZ Corporation manufacturers book cases that it sells for P65.00 each. It
costs XYZ P35,000 per year to operate its plant. This sum includes rent,
depreciation charges on equipment and salary payments. If the cost to produce one
bookcase is P50.00, how many cases must be sold each year for XYZ to avoid
taking a loss?
a. 2334 c. 750
b. 539 d. 2233
244.) A telephone switchboard 100 pair cable can be made up with either enameled
wire or tinned wire. There will be 400 soldered connections. The cost of soldering
a connection on the enameled wire will be P1.65, on the tinned wire, it will be
P1.15. A 100 pair cable made up with enameled wire cost P0.55 per lineal foot and
those made up to tinned wire cost P0.76 per lineal foot. Determine the length of
cable run in feet so that the cost of each installation would be the same.
a. 1121.06 ft c. 864.92 ft
b. 1001.25 ft d. 952.38 ft
245.) A company which manufactures electric motors has a production capacity of
200 motors a month. The variable costs are P150 per motor. The average selling
price of the motor is P275. Fixed costs of the company amounts to P20,000 per
month which included taxes. The number of motors that must be sold each month
to break even is closest to:
a. 40 c. 80
b. 150 d. 160
246.) Steel drums manufacturer incurs a yearly fixed operating cost of P200,000.
Each drum manufactured cost P160 to produce and sells for P200. What is the

23
manufacturer’s break even sales volume in drum per year? If they could
manufacture 7,000 drums per year, determine the amount of profit or loss.
a. 1250 ; P70,000 c. 5,000 ; P80,000
b. 2500 ; P60,000 d. 1,000 ; P75,000
247.) A new Civil Engineer produces a certain construction ,material at a labor cost
of P16.20 per piece, material cost of P38.50per piece and variable cost of P7.40
per piece. The fixed charges on the business is P100,000 a month. If he sells the
finished product at P95.00 each, how many pieces must be manufactured each
month to break even?
a. 3040 c. 3004
b. 3400 d. 4300
248.) A manufacturer produces certain items at a labor cost per unit of P315,
material cost per unit of P100, variable cost of P3.00 each. If the item has a selling
price of P995, how many units must be sold to break even if the monthly overhead
is P461,600?
a. 800 c. 700
b. 600 d. 900
249.) A cement firm with production capacity of 130 tons per day (24 hrs) of
clinker has its burning zone about 45 tons of magnesium chrome bricks being
replaced periodically, depending on some operational factors and the life of the
bricks. If locally produced bricks cost costing P30,000 per ton and have a life of 6
months, determine the more economical bricks and by how much?
a. P6,075,000 c. P6,505,000
b. P6,750,000 d. P6,057,000
250.) An equipment installation job in the completion stage can be completed in 40
days of 8 hour day work, with 40 men working. With the contract expiring in 30
days, the mechanical engineer contractor decided to add 10 men on the job,
overtime not being permitted. If the liquidated damages is P2,000 per day of delay,
and the men are paid P80 per day, how much money would he save if he will add
workers?
a. P16,000 c. P16,500
b. P15,500 d. P16,000
251.) A fixed capital investment of P10,000,000 is required for a proposed
manufacturing plant and an estimated working capital of P2,000,000. Annual
depreciation is estimated to be 10% of the fixed capital investment. Determine the
rate of return on the total investment and the minimum pay out period if the annual
profit is P2,500,000.
a. 20.83% ; 2.86 c. 23.80% ;
6.28
b. 20.38% ; 2.68 d. 23.08% ;
6.66
252.) A 500kw electric lighting plant cost P95 per kw installed. Fixed charges is
14%, operating cost is P0.013 per kw-hr. The plant averages 150kw for 5000 hour
of the year, 420 kw for 1000 hour and 20kw for the remainder. What is the unit
cost of production of electric energy?
a. P0.0184 c. P0.1840
b. P0.1084 d. P0.8104
253.) A mechanical engineer who was awarded a P450,000 contract to install the
machineries of an oil mill failed to finish the work on time. As provided for in the
contract, he has to pay a daily penalty equivalent to one fourth of one percent per
day for the next ten days and one percent per day for every day thereafter. If the
total penalty was P60750, how many days was the completion of the contract
delayed?
254.) By selling balut at P5 per dozen, a vendor gains 20%. The cost of the eggs
rises by 12.5%. If he sells at the same price as before, find his new gain %.
a. 6.6% c. 7.7%
b. 5.5% d. 7.6%
255.) In a certain department store, the monthly salary of a saleslady is partly
constant and partly varies as the value of her sales for the month. When the value
of her sales for the month is P10,000, her salary for that month is P900, when her
monthly sales goes up to P12,000, her monthly salary goes up to P1,000. What
must be the value of her sales for the month so that her salary for that month
would be P2,000?
a. P32,000 c. P30,000
b. P35,000 d. P40,000
256.) An equipment installation job in the completion stage can be completed in 50
days of 8 hour day work, with 50 men working. With the contract expiring in 40
days, the mechanical engineer contractor decided to add 15 men on the job,
overtime not being permitted. If the liquidated damages is P5,00 per day of delay,
and the men are paid P150 per day, how much money would he save with the
additional workers?
a. P44750 c. P44570
b. P47540 d. P45407
257.) Jojo bought a second hand Betamax VCR and then sold it to Rudy at a profit
of 40%; Rudy then sold the VCR to Noel at a profit of 20%. If Noel paid P2,856
more than it cost Jojo, how much did Jojo pay for the unit?

23
a. P4200 c. P2400
b. P4400 d. P2200
258.) Dalisay Corporation’s gross margin is 45% of sales. Operating expenses such
as sales and administration are 15% of sales. Dalisay is in 40% tax bracket. What
percent of sales is their profit after taxes?
a. 18% c. 24%
b. 5% d. 0%
259.) A manufacturer of sports equipment produces tennis rackets for which there
is a demand of 200 per month. The production setup cost for each lot of racket is
O300. IN addition, the inventory carrying cost for each racket is P24 per year.
Using the Economic Order Quantity (EQQ) model, which is the best production
batch size fro the rackets?
260.) A manufacturing firm maintains one product assembly line to produce signal
generators. Weekly demand for the generators is 35 units. The line operates for 7
hours per day, 5 days per week. What is the maximum production time per unit in
hours required of the line to meet the demand?
a. 1 hour c. 3 hours
b. 0.75 hours d. 2.25 hours
261.) A businessman wishes to earn 7% on his capital after payment of taxes. If the
income from an available investment will be taxed at an average of 42%, what
minimum rate or return, before payment of taxes, must the investment offer to be
justified?
a. 12.1% c. 11.1%
b. 10.7% d. 12.7%
262.) A 200 hp generator is being considered for purchase. The generator will cost
P320,000 with a life expectancy of 10 years, with an efficiency of 82%. The
maintenance cost per year is P5,000. This generator is used for 300 hours per year
and the cost of fuel, oil is P0.12 per kilowatt-hour. (1hp = 0.746kw). Assuming the
generator will have no salvage value, what will be the monthly cost of maintaining
the generator?
a. P842.40 c. P786.40
b. P962.52 d. P695.40
263.) An engineer buys a machine costing P500,000. Compute the capitalized cost
if the machine has a life of 5 years and a salvage value of P80,000. Rate of interest
is 12% per annum.
a. P2,424,732 c. P2,431,643
b. P1,050,934 d. P5,124,153
264.) A project costing P250,000 yields a yearly benefit of P80,000 for a period of
10 years with no salvage value at an interest rate of 6%. What is the benefit cost
ratio?
a. 4.24 c. 2.36
b. 3.85 d. 4.30
265.) A company constructed its factory with a fixed capital investment of P120M.
The net income after the tax and depreciation is expected to be P23m per year.
Annual depreciation cost is 10 % of fixed capital investment. Determine the
payout period in years.
266.) A machinery costing P720,000 is estimated to have a book value of
P40,545.73 when retired at the end of 10 years. Depreciation cost is computed
using a constant percentage of the declining book value. What is the annual rate of
depreciation?
a. 20% c. 30%
b. 25% d. 35%
267.) An asset is purchased for P9,000. Its estimated economic life is 10 years
after which it will be sold for P1,000. Find the depreciation in the first three years
using straight line method.
a. P2,400.00 c. P2,250.00
b. P2,412.34 d. P2,450.00
268.) An engineer bought an equipment for P500,000. He spent an additional
amount of P30,000 for installation and other expenses. The estimated useful life of
the equipment is 10 years. The salvage value is x% of the first cost. Using the
straight line method of depreciation, the book value at the end of 5 years will be
P291,500. What is the value of x?
a. 20% c. 30%
b. 40% d. 10%
269.) The initial cost of a paint sand mill, including its installation is P800,000.
The BIR approved life of this machine is 10 years for depreciation. The estimated
salvage value of the mill is P50,000 and the cost of dismantling is estimated to be
P15,000. Using straight line depreciation, what is the annual depreciation charge?
a. P75,500 c. P76,500

23
b. P76,000 d. P77,000
270.) The initial cost of a paint sand mill, including its installation is P800,000.
The BIR approved life of this machine is 10 years for depreciation. The estimated
salvage value of the mill is P50,000 and the cost of dismantling is estimated to be
P15,000. Using straight line depreciation, what is book value of the machine at the
end of 6 years?
a. P341,000 c. P340,000
b. P343,000 d. P342,000
271.) A unit of welding machine cost P45,000 with an estimated life of 5 years. Its
salvage value is P2,500. Find its depreciation rate by straight line method.
a. 18.89% c. 19.58%
b. 19.21% d. 19.89%
272.) A tax and duty free importation of a 30hp sand mill for painting
manufacturing cost P360,000. Bank charges and brokerage cost P5,000.
Foundation and installation costs were P25,000. Other incidental expenses amount
to P20,000. Salvage value of the mills estimated to be P60,000 after 20 years. Find
the appraisal value of the mill using straight line depreciation at the end of 10
years.
a. P234,000 c. P234,500
b. P235,000 d. P235,500
273.) An equipment costs P10,000 with a salvage value of P500 at the end of 10
years. Calculate the annual depreciation cost by sinking fund method at 4%
interest.
a. P721.54 c. P791.26
b. P724.56 d. P721.76
274.) An equipment costs P50,000 with a salvage value of P250 at the end of 10
years. Calculate the annual depreciation cost by sinking fund method at 8%
interest.
a. P3123.53 c. P3434.22
b. P3223.75 d. P3241.24
275.) An asset is purchased for P12,000. Its estimated economic life is 20 years
after which it will be sold for P5,000. Find the depreciation in the first five years
using straight line method.
a. P1,750 c. P1,250
b. P1,412 d. P1,450
276.) What is the difference of the amount 5 years from now for a 12% simple
interest and 12% compound interest per year?(P8,000 accumulated)
a. P1298.73 c. P1224.97
b. P1281.24 d. P1862.76
277.) Find the discount if P5,500 is discounted for 9 months at 15% compounded
quarterly.
a. P2442.09 c. P1883.66
b. P1248.24 d. P2451.99
278.) Find the ordinary simple interest at 7.5% on P5000 and the corresponding
amount at the end of 59 days.
a. P2145.24 c. P5061.45
b. P2241.12 d. P5123.24
279.) Find the exact simple interest at 7.5% on P5000 and the corresponding
amount at the end of 59 days.
a. P5187.24 c. P5021.45
b. P5221.12 d. P5060.60
280.) If P1050 accumulate P1275 when invested at a simple interest for 3 years.
What is the rate of interest?
a. 4.21% c. 6.73%
b. 5.85% d. 7.14%
281.) Determine the exact simple interest on P5,000 investment for the period
from January 15, 1996 to October 12, 1996 of the rate of interest in 18%.
a. P666.39 c. P632.40
b. P621.22 d. P636.29
282.) The exact simple interest of P5000, invested from June 21, 1995 to
December 25, 1995, is P100. What is the rate of interest?
a. 2.4% c. 2.7%
b. 3.2% d. 3.9%
283.) The amount of P50,000 was deposited in the bank earning at 7.5% per
annum. Determine the total amount at the end of 5 years if the principle and
interest were not withdrawn during the period.

23
a. P71,781.47 c. P70,024.29
b. P24,257.75 d. P29,240.99
284.) Determine the future amount of P100 for 10.25 years at a rate of 5%
compounded monthly.
a. P166.77 c. P163.12
b. P224.09 d. P214.12
compounded quarterly.
a. P124.02 c. P182.42
b. P166.42 d. P175.10
compounded semi-annually.
a. P153.29 c. P169.22
b. P165.90 d. P173.24
compounded daily.
a. P129.24 c. P195.32
b. P166.94 d. P128.87
288.) What is the present worth of a P500 annuity starting at the end of the third
year and continuing to the end of the fourth year, if the annual interest rate is 10%?
a. P717.17 c. P720.24
b. P252.91 d. P287.09
289.) Today a businessman borrowed money to be paid in 10 equal payments for
10 quarters. If the interest rate is 10% compounded quarterly and the quarterly
payment is P2,000, how much did he borrow?
a. P24214.23 c. P15125.24
b. P24311.53 d. P17504.13
290.) What annuity is required over 12 years to equate with a future amount of
P20,000? Assume i=6% annually.
a. P1121.24 c. P2314.12
b. P1244.22 d. P1185.54
291.) Find the annual payment to extinguish a debt of P10,000 payable for 6 years
at 12% interest annually.
a. P2214.42 c. P2525.24
b. P2432.26 d. P2044.83
292.) A bond issue of P50,000 in 10 years, bonds in P1000 units paying 10%
interest in annual payments, must be retired by the use of sinking fund which earns
8% compounded annually. What is the total cost for the interest ad retirement of
the entire bond issue.
a. P82,241 c. P82,214
b. P84,150 d. P84,510
293.) Determine the amount of interest you would receive per period if you
purchase a 6%, P5000 bond which matures in 10 years with interest payable
quarterly.
a. P24 c. P75
b. P98 d. P52
294.) A corporation floats callable bonds amounting to P100,000 each having a par
value of P500, the bond rate is 7.5% and the bonds are to be retired in 5 years, the
annual payments being as nearly equal as possible. What is the total payment for
the whole period of 5 years?
a. P123,625 c. P214,124
b. P124,241 d. P923,124
295.) A book store purchased the best selling book at P200. At what price should
this book be sold so that by giving a 20% discount, the profit is 30%.
a. P200 c. P400
b. P300 d. P500
296.) The selling price of a tv set is double that of its net cost. If the tv set is sold
to a customer at a profit of 25% of the net cost, how much discount was given to
the customer?
a. 35.8% c. 34.5%
b. 37.5% d. 44.5%
297.) A manufacturing firm maintains one product assembly line to produce signal
generators. Weekly demand for the generators is 35 units. The line operates for 7
hours per day, 5 days per week. What is the maximum production time per unit in
hours required of the line to meet the demand?

23
a. 1 hour c. 3 hours
b. 2 hours d. 4 hours
298.) Mahusay Corporation’s gross margin is 55% of sales. Operating expenses
such as sales and administration are 5% of sales. Mahusay is in 40% tax bracket.
What percent of sales is their profit after taxes?
a. 20% c. 40%
b. 30% d. 50%
299.) How much money must you invest in order to withdraw P5000 annually for
20 years if the interest rate is 12%?
a. P37,347.22 c. P38,243.29
b. P23,325.23 d. P27,124.09
300.) If interest is at rate of 10% compounded semi-annually, what sum must be
invested at the end of each 6 months to accumulate a fund of P12,000 at the end of
8 years?
a. P507.24 c. P247.24
b. P451.24 d. P694.92
Differential Calculus
301.) Find two numbers whose sum is 20, if the product of one by the cube of
another is to be the maximum.
a. 5 and 15 c. 4 and 16
b. 10 and 10 d. 8 and 12
302.) The sum of two numbers is 12. Find the minimum value of the sum of their
cubes.
a. 432 c. 346
b. 644 d. 244
303.) A printed page must contain 60sq.m. of printed material. There are to be
margins of 5cm. on either side and the margins of 3cm. on top and bottom. How
long should the printed lines be in order to minimize the amount of paper used?
a. 10 c. 12
b. 18 d. 15
304.) A school sponsored trip will cost each student 15 pesos if not more than 150
students make the trip. However, the cost will be reduced by 5 centavos for each
student in excess of 150. How many students should make the trip in order for the
school to receive the largest group income?
a. 225 c. 200
b. 250 d. 195
305.) A rectangular box with square base and open at the top is to have a capacity
of 16823cu.cm. Find the height of the box that requires minimum amount of
material required.
a. 16.14cm c. 12.14cm
b. 14.12cm d. 10.36cm
306.) A closed cylindrical tank has a capacity of 576.56 cubic meters. Find the
minimum surface area of the tank.
a. 383.40 cubic meters c. 516.32 cubic meters
b. 412.60 cubic meters d. 218.60 cubic meters
For Problems 307-309:
Two vertices of a rectangle are on the x axis. The other two vertices are on the
lines whose equations are y=2x and 3x+y=30.
.
307.) If the area of the rectangle is maximum, find the value of y.
a. 8 c. 9
b. 7 d. 6
308.) Compute the maximum area of the rectangle.
a. 30 sq. units c. 90 sq. units
b. 70 sq. units d. 40 sq. units
309.) At what point from the intersection of the x and y axes will the farthest
vertex of the rectangle be located along the x axis so that its area is max.
310.) A wall 2.245m high, is “x” meters away from a building. The shortest ladder
that can reach the building with one end resting on the ground outside the wall is
6m. What is the value of x?
a. 2 m c. 6 m

23
b. 4 m d. 8 m
311.) With only 381.7 square meter of materials, a closed cylindrical tank of
maximum volume. What is to be the height of the tank in m?
a. 9 m c. 11 m
b. 7 m d. 13 m
312.) If the hypotenuse of a right triangle is known, what is the ratio of the base
and the altitude of the right triangle when its area is maximum?
a. 1:1 c.
1:3
b. 1:2 d.
1:4
313.) What is the maximum length of the perimeter if the hypotenuse of a right
triangle is 5m long?
a. 12.08 m c. 20.09 m
b. 15.09 m d. 8.99 m
314.) An open top rectangular tank with square bases is to have a volume of 10
cubic meters. The material for its bottom is to cost 15 cents per square meter and
that for the sides 6 cents per square meter. Find the most economical dimension for
the tank.
a. 2 x 2 x 2.5 c. 2 x 3 x 2.5
b. 2 x 5 x 2.5 d. 2 x 4 x 2.5
315.) A trapezoidal gutter is to be made from a strip of metal 22m wide by bending
up the sides. If the base is 14m, what width across the top gives the greatest
carrying capacity?
a. 16 c. 10
b. 22 d. 27
316.) Divide the number 60 into two parts so that the product P of one part and the
square of the other is the maximum. Find the smallest part.
a. 20 c. 10
b. 22 d. 27
317.) The edges of a rectangular box are to be reinforced with narrow metal strips.
If the box will have a volume of 8 cubic meters, what would its dimension be to
require the least total length of strips?
a. 2 x 2 x 2 c. 3 x 3 x 3
b. 4 x 4 x 4 d. 2 x 2 x 4
318.) A rectangular window surmounted by a right isosceles triangle has a
perimeter equal to 54.14m. Find the height of the rectangular window so that the
window will admit the most light.
a. 10 c. 12
b. 22 d. 27
319.) A normal widow is in the shape of a rectangle surrounded by a semi-circle. If
the perimeter of the window is 71.416, what is the radius and the height of the
rectangular portion so that it will yield a window admitting the most light.
a. 20 c. 12
b. 22 d. 27
320.) Find the radius of a right circular cone having a lateral area of 544.12 sq. m.
to have a maximum value.
a. 10 c. 17
b. 20 d. 19
321.) A gutter with trapezoidal cross section is to be made from a long sheet of tin
that is 15 cm. wide by turning up one third of its width on each side. What is the
width across the top that will give a maximum capacity?
a. 10 c. 15
b. 20 d. 13
322.) A piece of plywood for a billboard has an area of 24 sq. feet. The margins at
the top and bottom are 9 inches and at the sides are 6 in. Determine the size of the
plywood for maximum dimensions of the painted area.
a. 4x6 c. 4x8
b. 3x4 d. 3x8
323.) A manufacturer estimates that the cost of production of “x” units of a certain
item is C=40x-0.02x2
-600. How many units should be produced for minimum
cost?
a. 1000 units c.
10 units

23
324.) If the sum of the two numbers is 4, find the minimum value of the sum of
their cubes.
a. 16 c. 10
b. 18 d. 32
325.) If x units of a certain item are manufactured, each unit can be sold for 200-
0.01x pesos. How many units can be manufactured for maximum revenue? What
is the corresponding unit price?
a. 10000,P100 c. 20000,P200
b. 10500,P300 d. 15000,P400
326.) A certain spare parts has a selling price of P150 if they would sell 8000 units
per month. If for every P1.00 increase in selling price, 80 units less will be sold
out per month. If the production cost is P100 per unit, find the price per unit for
maximum profit per month.
a. P175 c. P150
b. P250 d. P225
327.) The highway department is planning to build a picnic area for motorist along
a major highway. It is to be rectangular with an area of 5000 sq. m. is to be fenced
off on the three sides not adjacent to the highway. What is the least amount of
fencing that will be needed to complete the job?
a. 200 m. c. 400 m.
b. 300 m. d. 500 m.
328.) A rectangular lot has an area of 1600 sq. m. find the least amount of fence
that could be used to enclose the area.
a. 160 m. c. 100 m.
b. 200 m. d. 300 m.
329.) A student club on a college campus charges annual membership dues of P10,
less 5 centavos for each member over 60. How many members would give the club
the most revenue from annual dues?
a. 130 members c. 240
members
b. 420 members d. 650
members
330.) A monthly overhead of a manufacturer of a certain commodity is P6000 and
the cost of the material is P1.0 per unit. If not more than 4500 units are
manufactured per month, labor cost is P0.40 per unit, but for each unit over 4500,
the manufacturer must pay P0.60 for labor per unit. The manufacturer can sell
4000 units per month at P7.0 per unit and estimates that monthly sales will rise by
100 for each P0.10 reduction in price. Find the number of units that should be
produced each month for maximum profit.
331.) A company estimates that it can sell 1000 units per week if it sets the unit
price at P3.00, but it’s weekly sales will rise by 100 units for each P0.10 decrease
in price. Find the number of units sold each week and its unit price per maximum
revenue.
a. 2000 ; P2.00 c. 2500 ; P2.50
b. 1000 ; P3.00 d. 1500 ; P1.50
332.) In manufacturing and selling “x” units of a certain commodity, the selling
price per unit is P=5-0.002x and the production cost in pesos is C=3+1.10x.
Determine the production level that will produce the maximum profit and what
would this profit be?
a. 975, P1898.25 c. 865, P1670.50
b. 800, P1750.75 d. 785, P1920.60
333.) ABC company manufactures computer spare parts. With its present
machines, it has an output of 500 units annually. With the addition of the new
machines, the company could boost its yearly production to 750 units. If it
produces “x: parts it can set a price of P=200-0.15x pesos per unit and will have a
total yearly cost of C=6000+6x+0.003x2
in pesos. What production level
maximizes total yearly profit?
a. 660 units c.
560 units
b. 237 units d.
243 units
334.) The hypotenuse of a right triangle is 20cm. What is the maximum possible
area of the triangle in square centimeters?
a. 100 c.
120
b. 170 d.
160
335.) Sand is falling off a conveyor onto a conical pile at the rate of 15cm3
/min.
The base of the cone is approximately twice the altitude. Find the height of the pile
if the height of the pile is changing at the rate 0.047746 cm/min.
a. 10cm c. 8cm
b. 12cm d. 6cm

23
336.) A machine is rolling a metal cylinder under pressure. The radius of the
cylinder is decreasing at the rate of 0.05cm per second and the volume V is 128π
cu.cm. At what rate is the length “h” changing when the radius is 2.5 cm.
a. 0.8192 cm/sec c. 0.6178 cm/sec
b. 0.7652 cm/sec d. 0.5214 cm/sec
337.) Two sides of a triangle are 15cm and 20cm long respectively. How fast is the
third side increasing if the angle between the given sides is 60º and is increasing at
the rate of 2º/sec.
a. 0.05 cm/sec c. 1.20 cm/sec
b. 2.70 cm/sec d. 3.60 cm/sec
338.) Two sides of a triangle are 30cm and 40cm respectively. How fast is the area
of the triangle increasing if the angle between the given sides is 60º and is
increasing at the rate of 4º/sec.
a. 20.94 m2
/sec c. 14.68 m2
/sec
b. 29.34 m2
/sec d. 24.58 m2
/sec
339.) A man 6ft tall is walking toward a building at the rate of 5ft/sec. If there is a
light on the ground 50ft from the building, how fast is the man/s shadow on the
building growing shorter when he is 30ft from the building?
a. -3.75 fps c. -5.37 fps
b. -7.35 fps d. -4.86 fps
340.) The volume of the sphere is increasing at the rate of 6cm3
/hr. At what rate is
its surface area increasing when the radius is 50cm(in cm3
/hr)
a. 20.94 m2
/sec c. 14.68 m2
/sec
b. 29.34 m2
/sec d. 24.58 m2
/sec
341.) A particle moves in a plane according to the parametric equations of
motions: x=t2
, y=t3
. Find the magnitude of the acceleration when the t=0.6667.
a. 6.12 c. 4.90
b. 5.10 d. 4.47
342.) The acceleration of the particle is given by a=2+12t in m/s2
where t is the
time in minutes. If the velocity of this particle is 11m/s after 1min, find the
velocity after 2mins.
a. 31 m/sec c. 37 m/sec
b. 45 m/sec d. 26 m/sec
343.) A particle moves along a path whose parametric equations are x=t3 and
y=2t2. What is the acceleration when t=3sec?
a. 15.93 m/sec2
c. 23.36m/sec2
b. 18.44 m/sec2
d. 10.59 m/sec2
344.) A vehicle moves along a trajectory having coordinates given as x=t3
and y=1-
t2
. The acceleration of the vehicle at any point of the trajectory is a vector, having
magnitude and direction. Find the acceleration when t=2.
a. 13.20 c. 15.32
b. 12.17 d. 12.45
345.) Y = x3
– 3x. Find the maximum value of y.
a. 2 c. 0
b.1 d. 3
346.) Find the radius of curvature of the curve y=2x3
+3x2
at (1,5).
a. 90 c. 95
b. 97 d. 84
347.) Compute the radius of curvature of the curve x=2y3
-3y2
at (4, 2).
a. -99.38 c. -95.11
b.- 97.15 d. -84.62
348.) Find the radius of curvature of a parabola y2
-4x=0 at point (4, 4).
a. 25.78 c. 20.33
b. 22.36 d. 15.42
349.) Find the radius of curvature of the curve x=y3
at point (1, 1).
a. -1.76 c. 2.19
b. -1.24 d. 2.89
350.) Find the point of inflection of the curve y=x3
-3x2
+6.
a. (1, 4) c. (0, 2)
b. (1,3) d. (2, 1)

23
Integral Calculus
351.) Find the total length of the curve r=4(1-Sinθ) from θ=90º to θ=270º and also
the total perimeter of the curve.
a. 18, 36 c. 12, 24
b. 16, 32 d. 15, 30
352.) Find the length of the curve r=4Sin θ from θ=0º to θ=90º and also the total
length of curve.
a. 2π ; 4π c. π ; 2π
b. 3π ; 6π d. 4π ; 8π
353.) Find the length of the curve r = a (1-Cosθ) from θ=0º to θ=π and also the
total length of the curve.
a. 4a ; 8a c. 3a ; 6a
b. 2a ; 4a d. 5a ; 9a
354.) Find the total length of the curve r = a Cosθ.
a. 2πa c. 1.5πa
b. πa d. 0.67πa
355.) Find the length of the curve having a parametric equations of x = a Cos3
θ, y
= a Sin2
θ from θ=0º to θ=2π.
a. 5a c. 7a
b. 6a d. 8a
356.) Find the centroid of the area bounded by the curve y=4-x2
, the line x=1 and
the coordinate axes.
a. (0.48, 1.85) c.
(0.24, 1.57)
b. (1.22, 0.46) d.
(2.16, 0.53)
357.) Find the centroid of the area under y=4-x2
in the first quadrant.
a. (0.75, 1.6) c.
(0.74, 1.97)
b. (1.6, 0.95) d.
(3.16, 2.53)
358.) Find the centroid of the area in first quadrant bounded by the curve y2
=4ax
and the latus rectum.
a. (0.6a, 0.75a) c. (0.94a,
2.97a)
b. (1.23a, 0.95a) d. (1.16a,
0.53a)
359.) A triangular section has coordinates of A(2,2), B(11,2), and C(5,8). Find the
coordinates of the centroid of the triangular section.
a. (7, 4) c.
(8, 4)
b. (6, 4) d.
(9, 4)
360.) The following cross section has the following given coordinates. Compute
for the centroid of the given cross section. A(2,2), B(5,8), C(7,2), D(2,0), and
E(7,0).
a. (4.6, 3.4) c.
(5.2, 3.8)
b. (4.8, 2.9) d.
(5.3, 4.1)
361.) Sections ABCD is a quadrilateral having the given coordinates A(2,3),
B(8,9), C(11,3), and D(11,0). Compute for the coordinates of the centroid of the
quadrilateral.
a. (7.33, 4) c. (5.32, 3)
b. (6.23, 4) d. (8.21, 3)
362.) A cross section consists of a triangle and a semi circle with AC as its
diameter. If the coordinates of A(2,6), B(11,9), and C(14,6). Compute for the
coordinates of the centroid of the cross section.
a. (4.6, 3.4) c.
(5.2, 3.8)
b. (4.8, 2.9) d.
(5.3, 4.1)
363.) A 5m x 5cm is cut from a corner of 20cm x 30cm cardboard. Find the
centroid from the longest side.
a. 10.33m c. 10.99m
b. 11.42m d. 12.42m

23
364.) Locate the centroid of the area bounded by the parabola y2
=4x, the line y=4
and the y-axis.
a. (1.2, 3) c. (0.6, 3)
b. (0.4, 3) d. (1.33, 3)
365.) Find the centroid of the area bounded by the curve x2
=-(y-4), the x-axis and
the y-axis on the first quadrant.
a. (0.75, 1.6) c.
(1.75, 1.2)
b. (1.25, 1.4) d.
(0.25, 1.8)
366.) Locate the centroid of the area bounded by the curve y2
=-1.5(x-6), the x-axis
and the y-axis on the first quadrant.
a. (2.4, 1.13) c.
(2.8, 0.63)
b. (2.6, 0.88) d.
(2.2, 1.38)
367.) Locate the centroid of the area bounded by the curve 5y2
=16x and y2
=8x-24
on the first quadrant.
a. (2.20, 1.51) c.
(2.78, 1.39)
b. (1.50, 0.25) d.
(1.64, 0.26)
368.) Locate the centroid of the area bounded by the parabolas x2
=8y and x2
=16(y-
2) in the first quadrant.
a. (3.25, 1.2) c.
(2.67, 2.0)
b. (2.12, 1.6) d.
(2.00, 2.8)
369.) Given the area in the first quadrant bounded by x2
=8y, the line y-2=0 and the
y-axis. What is the volume generated when revolved about the line y-2=0?
a. 53.31m3
c. 26.81m3
b. 45.87m3
d. 33.98m3
=8y, the line x=4 and the x-
axis. What is the volume generated by revolving this area about the y-axis?
a. 78.987m3
c.
61.253m3
b. 50.265m3
d.
82.285m3
=8y, the line y-2=0 and the
y-axis. What is the volume generated when this area is revolved about the x-axis.
a. 20.32m3
c. 40.21m3
b. 34.45m3
d. 45.56m3
372.) Find the volume formed by revolving the hyperbola xy=6 from x=2 to x=4
about the x-axis.
a. 28.27m3
c. 23.23m3
b. 25.53m3
d. 30.43m3
373.) The region in the first quadrant under the curve y=Sinh x from x=0 to x=1 is
revolved about the x-axis. Compute the volume of solid generated.
a. 1.278m3
c. 3.156m3
b. 2.123m3
d. 1.849m3
374.) A square hole of side 2cm is chiseled perpendicular to the side of a
cylindrical post of radius 2cm. If the axis of the hole is going to be along the
diameter of the circular section of the post, find the volume cutoff.
a. 15.3m3
c. 43.7m3
b. 23.8m3
d. 16.4m3
375.) Find the volume common to the cylinders x2
+y2
=9 and y2
+z2
=9.
a. 241m3
c. 424m3
b. 533m3
d. 144m3
376.) Given is the area in the first quadrant bounded by x2
=8y, the line, the line
x=4 and the x-axis. What is the volume generated by revolving this area about the
y-axis.
a. 50.26m3
c. 53.26m3
b. 52.26m3
d. 51.26m3
377.) The area bounded by the curve y2
=12x and the line x=3 is revolved about the
line x=3. What is the volume generated?
a. 185 c. 181

23
b. 187 d. 183
378.) The area in the second quadrant of the circle x2
+y2
=36 is revolved about the
line y+10=0. What is the volume generated?
a. 2128.63 c. 2233.43
b. 2228.83 d. 2208.53
379.) The area enclosed by the ellipse 0.11x2
+0.25y2
=1 is revolved about the line
x=3, what is the volume generated?
a. 370.3 c. 355.3
b. 360.1 d. 365.1
380.) Find the volume of the solid formed if we rotate the ellipse 0.11x2
+0.25y2
=1
about the line 4x+3y=20.
a. 48 π2
m3
c. 40 π2
m3
b. 45π2
m3
d. 53 π2
m3
381.) The area on the first and second quadrant of the circle x2
+y2
=36 is revolved
about the line x=6. What is the volume generated?
a. 2131.83 c. 2421.36
b. 2242.46 d. 2342.38
382.) The area on the first quadrant of the circle x2
+y2
line x=5. What is the volume generated?
a. 355.31 c. 368.33
b. 365.44 d. 370.32
383.) The area of the second and third quadrant of the circle x2
+y2
=36 is revolved
about the line x=4. What is the volume generated?
a. 2320.30 c. 2327.25
b. 2545.34 d. 2520.40
384.) The area on the first quadrant of the circle x2
+y2
line y+10=0. What is the volume generated?
a. 3924.60 c. 2593.45
b. 2229.54 d. 2696.50
385.) The area enclosed by the ellipse 0.0625x2
+0.1111y2
=1 on the first and 2nd
quadrant, is revolved about the x-axis. What is the volume generated?
a. 151.40 c. 156.30
b. 155.39 d. 150.41
386.) The area enclosed by the curve 9x2
+16y2
=144 on the first quadrant, is
revolved about the y-axis. What is the volume generated?
a. 100.67 c. 98.60
b. 200.98 d. 54.80
387.) Find the volume of an ellipsoid having the equation
0.04x2
+0.0625y2
+0.25z2
=1.
a. 167.55 c. 171.30
b. 178.40 d. 210.20
388.) Find the volume of a spheroid having equation 0.04x2
+0.111y2
+0.111z2
=1.
a. 178.90 c. 188.50
b. 184.45 d. 213.45
389.) The region in the first quadrant which is bounded by the curve y2
=4x, and
the lines x=4 and y=0, is revolved about the x-axis. Locate the centroid of the
resulting solid revolution.
a. 2.667 c. 1.111
b. 2.333 d. 1.667
390.) The region in the first quadrant, which is bounded by the curve x2
=4y, the
line x=4, is revolved about the line x=4. Locate the centroid of the resulting solid
revolution.
a. 0.8 c.
1.0
b. 0.5 d.
0.6
391.) The area bounded by the curve x3
=y, the line y=8 and the y-axis, is to be
revolved about the y-axis. Determine the centroid of the volume generated.
a. 5 c. 4
b. 6 d. 7

23
392.) The area bounded by the curve y=x3
and the x-axis. Determine the centroid
of the volume generated.
a. 2.25 c. 1.25
b. 1.75 d. 0.75
393.) Find the moment of inertia of the area bounded by the curve x2
=4y, the line
y=1 and the y-axis on the first quadrant with respect to x-axis.
a. 1.2 c.
0.57
b. 3.5 d.
1.14
=4y, the line
y=1 and the y-axis on the first axis with respect to y axis.
a. 6.33 c.
0.87
b. 1.07 d.
0.94
=8y, the line
x=4, and the x-axis on the first quadrant with respect to x-axis.
a. 1.52 c.
1.98
b. 2.61 d.
2.36
=8y, the line
x=4, and the x-axis on the first quadrant with respect to y-axis.
a. 25.6 c. 31.6
b. 21.8 d.
36.4
397.) Find the moment of inertia of the area bounded by the curve y2
=4x, the line
x=1, and the x-axis on the first quadrant with respect to x-axis.
a. 1.067 c. 1.861
b. 1.142 d. 1.232
=4x, the line
x=1, and the x-axis on the first quadrant with respect to y-axis.
a. 0.571 c. 0.436
b. 0.682 d. 0.716
=4x, the line
y=2, and the y-axis on the first quadrant with respect to y-axis.
a. 0.095 c. 0.088
b. 0.064 d. 0.076
400.) Find the moment of inertia with respect to x-axis of the area bounded by the
parabola y2
=4x, the line x=1.
a. 2.35 c.
2.13
b. 2.68 d.
2.56

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