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# Lesson 7.8

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### Lesson 7.8

1. 1. Simple and Compound Interest J8
2. 2. Simple Interest <ul><li>When you first deposit money in a savings account, your deposit is called - PRINCIPAL . </li></ul><ul><li>The bank takes the money and invests it. </li></ul><ul><li>In return, the bank pays you INTEREST based on the INTEREST RATE. </li></ul><ul><li>Simple interest - interest paid only on the PRINCIPAL. </li></ul>
3. 3. Ex. 1 Simple Interest Formula <ul><li>I = prt </li></ul><ul><li>I = interest </li></ul><ul><li>P = principal </li></ul><ul><li>R = the interest rate per year </li></ul><ul><li>T = the time in years . </li></ul>
4. 4. Real-World <ul><li>Suppose you deposit \$400 in a savings account. The interest rate is 5% per year. </li></ul><ul><li>a. Find the interest earned in 6 years. Find the total of principal plus interest. </li></ul><ul><li>I = P R T  Formula </li></ul><ul><li>P = 400 , R = 0.05 = 5% , T = 6 (in years) </li></ul><ul><li>400 x 0.05 = 20 = interest on one year </li></ul><ul><li>400 x 0.05 x 6 = 120 = interest on \$400 over 6 years </li></ul><ul><li>400 + 120 = \$520 = amount in account after 6 years. </li></ul>
5. 5. b. Now Figure Interest In Months <ul><li>Remember that T = time in Years . </li></ul><ul><li>Find the interest earned in three months. Find the total of principal plus interest. </li></ul><ul><li>What fraction of a year is 3 months ? </li></ul><ul><li>T = 3/12 = ¼ or 0.25 </li></ul><ul><li>I = PRT </li></ul><ul><li>I = 400 x 0.05 x 0.25 </li></ul><ul><li>I = \$5 = interest earned after 3 months </li></ul><ul><li>\$5 + \$400 = total amount in account </li></ul><ul><li>\$405 </li></ul>
6. 6. Now you try! Find the Simple Interest <ul><li>1. </li></ul><ul><li>Principal = \$250 </li></ul><ul><li>Interest Rate = 4% </li></ul><ul><li>Time = 3 Years </li></ul><ul><li>2. </li></ul><ul><li>Principal = \$250 </li></ul><ul><li>Interest Rate = 3.5% </li></ul><ul><li>Time = 6 Months </li></ul>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. 7. Ex. 2 Compound Interest <ul><li>Compound Interest - when the bank pays interest on the Principal AND the Interest already earned. </li></ul><ul><li>Balance - the Principal PLUS the Interest. </li></ul><ul><li>The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest. </li></ul>
8. 8. <ul><li>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. </li></ul>
9. 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. 10. Compound Interest Formula <ul><li>You can find a balance using compound interest in one step with the compound interest formula. </li></ul><ul><li>INTEREST PERIOD - the length of time over which interest is calculated. </li></ul><ul><li>The Interest Period can be a year or less than a year. </li></ul>
11. 11. Compound Interest Formula <ul><li>B = p(1 + r) n </li></ul><ul><li>B = the final balance </li></ul><ul><li>P = is the principal </li></ul><ul><li>R = the interest rate for each interest period </li></ul><ul><li>N = the number of interest periods. </li></ul>
12. 12. Ex. 3 Semi-Annual <ul><li>When interest is compounded semiannually (twice per year), you must DIVIDE the interest rate by the number of interest periods, which is 2. </li></ul>6% annual interest rate ÷ 2 interest periods = 3% semiannual interest rate payment periods = number of years x number of interest periods per year.
13. 13. <ul><li>Find the balance on a deposit of \$1,000, earning 6% interest compounded semiannually for 5 years. </li></ul><ul><li>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. </li></ul><ul><li>Now plug it into the formula! </li></ul>
14. 14. The Formula! <ul><li>B = p (1 + R) n </li></ul><ul><li>B = \$1,000 (1 + 0.03) 10 </li></ul><ul><li>B = \$1,000 (1.03) 10 </li></ul><ul><li>B = \$1,000 (1.34391638) </li></ul><ul><li>B = \$1,343.92 </li></ul>
15. 15. Now you try! <ul><li>Find the balance for each account. Amount Deposited: \$900, Annual Interest Rate: 2%, Time: 3 Years. </li></ul><ul><li>3. Compounding Annually </li></ul><ul><li>4. Compounding Semiannually </li></ul>\$955.09 \$955.37