Lesson 7.8
- 1. Simple and Compound Interest J8
- 2. Simple Interest When you first deposit money in a savings account, your deposit is called - PRINCIPAL . The bank takes the money and invests it. In return, the bank pays you INTEREST based on the INTEREST RATE. Simple interest - interest paid only on the PRINCIPAL.
- 3. Ex. 1 Simple Interest Formula I = prt I = interest P = principal R = the interest rate per year T = the time in years .
- 4. Real-World Suppose you deposit $400 in a savings account. The interest rate is 5% per year. a. Find the interest earned in 6 years. Find the total of principal plus interest. I = P R T Formula P = 400 , R = 0.05 = 5% , T = 6 (in years) 400 x 0.05 = 20 = interest on one year 400 x 0.05 x 6 = 120 = interest on $400 over 6 years 400 + 120 = $520 = amount in account after 6 years.
- 5. b. Now Figure Interest In Months Remember that T = time in Years . Find the interest earned in three months. Find the total of principal plus interest. What fraction of a year is 3 months ? T = 3/12 = ¼ or 0.25 I = PRT I = 400 x 0.05 x 0.25 I = $5 = interest earned after 3 months $5 + $400 = total amount in account $405
- 6. Now you try! Find the Simple Interest 1. Principal = $250 Interest Rate = 4% Time = 3 Years 2. Principal = $250 Interest Rate = 3.5% Time = 6 Months Reminder: Time is always in terms of Years. So, if you’re dealing with months, you have to make your months a fraction of a year. $30 $4.38 I = PRT
- 7. Ex. 2 Compound Interest Compound Interest - when the bank pays interest on the Principal AND the Interest already earned. Balance - the Principal PLUS the Interest. The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest.
- 8. You deposit $400 in an account that earns 5% interest compounded annually (once per year). What is the balance in your account after 4 years? In your last calculation, round to the nearest cent.
- 9. Fill In This Chart $486.20 Year 4: Year 3: 420.00 Year 2: 400 + 20 = 420.00 400.00 · 0.05 = 20.00 Year 1: $400.00 Balance at End of Each Year Interest (I = PRT) Principle @ Beginning of Year
- 10. Compound Interest Formula You can find a balance using compound interest in one step with the compound interest formula. INTEREST PERIOD - the length of time over which interest is calculated. The Interest Period can be a year or less than a year.
- 11. Compound Interest Formula B = p(1 + r) n B = the final balance P = is the principal R = the interest rate for each interest period N = the number of interest periods.
- 12. Ex. 3 Semi-Annual When interest is compounded semiannually (twice per year), you must DIVIDE the interest rate by the number of interest periods, which is 2. 6% annual interest rate ÷ 2 interest periods = 3% semiannual interest rate payment periods = number of years x number of interest periods per year.
- 13. Find the balance on a deposit of $1,000, earning 6% interest compounded semiannually for 5 years. The interest rate R for compounding semiannually is 0.06 ÷2, or 0.03. The number of payment periods N is 5 years x 2 interest periods per year , or 10. Now plug it into the formula!
- 14. The Formula! B = p (1 + R) n B = $1,000 (1 + 0.03) 10 B = $1,000 (1.03) 10 B = $1,000 (1.34391638) B = $1,343.92
- 15. Now you try! Find the balance for each account. Amount Deposited: $900, Annual Interest Rate: 2%, Time: 3 Years. 3. Compounding Annually 4. Compounding Semiannually $955.09 $955.37