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# 7.8 Simple and Compound Interest

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Chapter 7, Section 8: Simple and Compounded Interest. Last section of Chapter 7.

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### 7.8 Simple and Compound Interest

1. 1. Chapter 7, Section 8: Simple and Compound Interest January 15 th , 2009 Total Real Life Stuff
2. 2. Warm Up: <ul><li>Find 6% of \$400. </li></ul><ul><li>Find 5% of \$2,000. </li></ul><ul><li>Find 4.5% of \$700. </li></ul><ul><li>Find 5.5% of \$325. </li></ul>\$24 \$100 \$31.50 \$17.88
3. 3. 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 is interest paid only on the PRINCIPAL. </li></ul>
4. 4. 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>
5. 5. Real-World <ul><li>Suppose you deposit \$400 in a savings account. The interest rate is 5% per year. </li></ul><ul><li>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>
6. 6. Now Figure Interest In Months <ul><li>Remember that T = time in Years . </li></ul><ul><li>So, 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>
7. 7. Try These: Both Find the Simple Interest <ul><li>Principal = \$250 </li></ul><ul><li>Interest Rate = 4% </li></ul><ul><li>Time = 3 Years </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
8. 8. Compound Interest <ul><li>Compound Interest is when the bank pays interest on the Principal AND the Interest already earned. </li></ul><ul><li>The Balance is 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>
9. 9. Compound Interest Example <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>
10. 10. Fill In This Chart \$486.20 Year 4: Year 3: Year 2: Year 1: \$400.00 Balance at End of Each Year Interest (I = PRT) Principle @ Beginning of Year
11. 11. 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>An INTEREST PERIOD is 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>
12. 12. 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>
13. 13. Semi-Annual <ul><li>When interested 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 To find the number of payment periods, multiply the number of years by the number of interest periods per year.
14. 14. Example <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>
15. 15. 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><ul><li>Happy? You’ll actually get to use a calculator for these =] </li></ul>
16. 16. Try These: Both <ul><li>Find the balance for each account. Amount Deposited: \$900, Annual Interest Rate: 2%, Time: 3 Years. </li></ul><ul><li>Compounding Annually </li></ul><ul><li>Compounding Semiannually </li></ul>\$955.09 \$955.37
17. 17. Assignment #59 <ul><li>HANDOUT!!! </li></ul>