Math 034 First Letter of Last Name Homework #7 .docx
- 1. Math 034 First Letter of Last Name Homework #7 Full Name ___________________________ Due Wednesday 10/28/15 Section _____________________________ 1. (Section 6.3) Suppose that Lily, Joshua, and Burt own a bike shop that they have set up as a business partnership. They agree to distribute their profits in unequal shares because Joshua works the most hours and Burt does the accounting. They agree to distribute the profits as follows: Lily (7 parts), Joshua (12 parts), Burt (11 parts). The bike shop earned $32,000 last month. How much does each person receive? 2. (Section 6.3) Fastlane Car Rental earned $835,000 in the last quarter, and the company’s management declared a dividend of $405,000. The company has 540,000 shares of stock issued. If you own 164 shares, how much will you receive as a dividend? 3. (Section 7.1) Mocha Crunch Bakery paid its shareholders a dividend of $1.12 per share in the last quarter and $4.25 per share in the last year. The market price per share of Mocha Crunch Bakery is currently $36.59. a. Calculate the stock’s current dividend yield. b. Calculate the stock’s trailing dividend yield.
- 2. 4. (Section 7.1) Eleven years ago, I invested $10,000 in the stock of Butterfly Hollow Corporation. I sold the stock today for $14,195. What compound annual growth rate does this represent? 5. (Section 7.1) Nine years ago, I bought stock in Clementine Enterprises for $20.25 per share. The stock has split 2 for 1 twice, and now trades for $14.05 per share. What compound annual growth rate does my capital gain represent? 6. (Section 7.1) Fifteen years ago, I invested $2,500 in a dividend reinvestment plan offered by my local electric utility company. The value of my original investment, including reinvested dividends, has grown to $4,746.16. What was my total rate of return? 7. (Section 7.2) On September 1, 2015, Havershire Inc. issued a $5,000 par value bond with a 3% coupon rate and a September 1, 2030 maturity date. Interest will be paid semiannually. How much total interest will the owner of this bond receive? 8. (Section 7.2) Viking Shield Solution
- 3. s issued a $2,000 par value bond with a 4 3/8% coupon rate. Interest payments are made semiannually. Suppose that one of these bonds sells for $1,950.79. What is the current yield? 9. (Section 7.2) Alicia’s grandmother bought a $100 face value savings bond for $50 when Alicia was born. On Alicia’s 21 st birthday, she cashed the bond in for $141.20. What effective rate of compound interest did she earn on this bond? Trial Balance-EntriesBig Ed's Motorcycle ShopEnd of Period WorksheetFor the period ending 12/31/2015Unadjusted Trial BalanceAdjusting EntriesAdjusted Trial BalanceIncome StatementBalance SheetDRCRDRCRDRCRDRCRDRCRCash184,500Accounts Receivable145,200Merchandise Inventory, Parts100,000Merchandise Inventory, Motorcycles110,000Office
- 4. Supplies6,720Prepaid Insurance4,080Office Equipment50,000Accumulated Depreciation-Office Equipment7,500Store Equipment52,000Accumulated Depreciation-Store Equipment7,860Shop Equipment183,600Accumulated Depreciation-Shop Equipment41,040Accounts Payable66,720Salaries PayableInterest PayableNote Payable (due 2010)67,200Ed Silver, Capital534,180Ed Silver, Drawing42,000Sales1,488,000Cost of Merchandise Sold930,000Sales Salaries Expense207,840Service Salaries Expense100,980Office Salaries ExpenseAdvertising Expense52,560Depreciation Expense-Office EquipmentDepreciation Expense-Store EquipmentDepreciation Expense-Shop EquipmentMiscellaneous Selling Expense1,920Rent Expense37,620Insurance Expense- 0Interest ExpenseOffice Supplies Expense1,560Miscellaneous Administrative Expense1,9202,212,5002,212,500JournalAdjusting EntriesDebitCreditJournalClosing EntriesDebitCredit 2014 PCTBBig Ed's Motorcycle ShopPost Closing Trial BalanceFor the period ended December 31, 20x7DRCRCash81,900Accounts Receivable179,200Merchandise Inventory, Parts115,000Merchandise Inventory, Motorcycles71,980Office Supplies4,220Prepaid Insurance1,880Office Equipment50,000Accumulated
- 5. Depreciation-Office Equipment7,500Store Equipment52,000Accumulated Depreciation-Store Equipment7,860Shop Equipment168,600Accumulated Depreciation-Shop Equipment41,040Accounts Payable65,000Salaries Payable7,500Interest Payable4,500Note Payable (due 2010)57,200Ed Silver, Capital534,180724,780724,780 MATH 034 Formulas Simple Interest Formula I = PRT I = simple interest P = principal R = simple interest rate T= term
- 6. Nth Term of An Arithmetic Sequence an = a1 + (n – 1)d a1 = first term d = common difference Sum of the First n Terms of an Arithmetic Sequence Sn = (n/2)(a1 + an) a1 = first term an = nth term Simple Discount Formula D = MdT D = simple discount M = maturity value
- 7. d = simple discount rate T = term Compound Interest Formula FV = PV(1 + i) n FV = future value PV = present value i = interest rate per compounding period n = number of compounding periods N+1 st Term of a Geometric Sequence an = a0 r n a0 = first term
- 8. a1 = second term r = common ratio = a1/a0 Sum of the First n Terms of a Geometric Sequence Sn = a0 (1 – r n ) / (1 – r) a0 = first term r = common ratio = a1/a0 Infinite Geometric Sum S∞ = a0 /(1 – r) a0 = first term r = common ratio = a1/a0
- 9. Compound Interest Rate i = compound interest rate FV = future value PV = present value n = number of compounding periods Time Periods n = log (FV/PV) log (1 + i) i = compound interest rate FV = future value PV = present value
- 10. Rule of 72 The time required for a sum of money to double at a compound interest rate of x% is approximately 72/x years. (x should not be converted to a decimal) Rule of 72 (Alternate Form) The compound interest rate required for a sum of money to double in x years is approximately 72/x percent.
- 11. Effective Interest Rate Eff. Rate = (1 + r/c) c – 1 r = the nominal interest rate c = the number of compoundings per year Continuous Compounding FV = PV e (rt) FV = future value PV = present value e = a mathematical constant (approx. 2.71828) r = annual interest rate t = number of years
- 12. Future Value Annuity Factor sn/i = i = interest rate per payment period n = number of payment periods Future Value of an Ordinary Annuity FV = PMTsn/i FV = future value of the annuity PMT = amount of each payment sn/i = annuity factor Future Value of an Annuity Due FV = PMTsn/i(1 + i) FV = future value of the annuity PMT = amount of each payment i = interest rate per payment period sn/i = annuity factor
- 13. Interest for Future Value Annuities interest = FV – total deposits Present Value Annuity Factor i = interest rate per payment period n = number of payment periods Present Value of an Ordinary Annuity PV = PMTan/i PV = present value of the annuity PMT = amount of each payment an/i = present value annuity factor Present Value of an Annuity Due PV = PMTan/i(1 + i)
- 14. PV = present value of the annuity PMT = amount of each payment an/i = present value annuity factor Interest for Present Value Annuities interest = total deposits – PV 1/ ( ) 1 nFV i PV i
- 16. Sales Tax T = P(1 + r) T = total price including tax P = price before tax r = sales tax rate T – P = amount of tax Income Tax Formulas Annual taxable income = annual income – benefits – exemptions – deductions Paycheck taxable income = paycheck income – benefits – exemptions
- 17. FICA taxes based on paycheck income – benefits Dividends dividend per share = total dividend total # shares individual dividend = (dividend per share)(# individual shares) current dividend yield = quarterly dividend per share × 4 market price per share trailing divided yield = trailing dividend per share market price per share
- 18. Compound Annual Growth Rate or Rate of Return i = compound growth rate FV = future value PV = present value n = number of years Net Asset Value (NAV) NAV = total assets / total number of shares Mutual Fund Shares # shares = amount invested / NAV
- 19. Inflation Formula FV = PV(1 + i) n FV = future value of an item PV = present value of an item i = rate of inflation n = number of time periods Declining Balance Depreciation FV = PV(1 + i) n FV = future value PV = present value i = depreciation rate n = years
- 20. Straight Line Depreciation Total depreciation amount = Original value – Residual value Annual depreciation = Total depreciation amount Useful Life Depreciated value = Original value – (# of years)(Annual depreciation) Credit Card Interest I = PRT I = interest P = principal
- 21. R = interest rate T= term Mortgage Formulas Equity = value of home – amount of mortgage Total PITI = principal + interest + taxes + insurance(s) One point = 1% of the amount of the loan Payback period = cost of points / monthly savings The 28% Rule Total PITI cannot exceed 28% of gross monthly income. The 36% Rule Total PITI and all other long-term debt payments cannot
- 22. exceed 36% of gross monthly income. Lease Payment = Payment on Loss + Interest on Residual Payment on loss: Use PV = PMTan/i where PV = original price – residual value Interest on residual: Use I=PRT where P = residual value Markup Based on Cost P = C(1 + r) P = selling price C = cost r = percent markup
- 23. Markup Based on Selling Price C=SP(1 – r) C = item’s cost SP = selling price r = gross profit margin Markdown MP = OP(1 – d) MP = marked-down price OP = original price d = percent markdown Profit Margin Formulas Gross profit = sales – cost Gross profit margin = gross profit / sales
- 24. Gross profit = (gross profit margin)(sales) Net profit = sales – cost – expenses Net profit margin = net profit / sales Cost-Revenue Analysis P = R – C P = profit function R = revenue function C= cost function 1/ ( ) 1 nFV i
- 25. PV