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# Simple and compound interest student

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### Simple and compound interest student

1. 1. Simple and Compound Interest
2. 2. Warm Up:  Find 6% of \$400.  Find 5% of \$2,000.  Find 4.5% of \$700.  Find 5.5% of \$325.
3. 3. 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 is interest paid only on the PRINCIPAL.
4. 4. Simple Interest Formula I = prt I = interest P = principal R = the interest rate per year T = the time in years.
5. 5. Real-World  Suppose you deposit \$400 in a savings account. The interest rate is 5% per year.  Find the interest earned in 6 years. Find the total of principal plus interest.  I = PRT  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.
6. 6. Now Figure Interest In Months  Remember that T = time in Years.  So, 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
7. 7. Try These: Both Find the Simple Interest  Principal = \$250  Interest Rate = 4%  Time = 3 Years  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.
8. 8. Compound Interest  Compound Interest is when the bank pays interest on the Principal AND the Interest already earned.  The Balance is the Principal PLUS the Interest.  The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest.
9. 9. Compound Interest Example  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.
10. 10. Fill In This Chart Principle @ Beginning of Year Year 1: \$400.00 Year 2: Year 3: Year 4: Interest (I = PRT) Balance at End of Each Year
11. 11. Compound Interest Formula  You can find a balance using compound interest in one step with the compound interest formula.  An INTEREST PERIOD is the length of time over which interest is calculated.  The Interest Period can be a year or less than a year.
12. 12. 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.
13. 13. Semi-Annual  When interested 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 To find the number of payment periods, multiply the number of years by the number of interest periods per year.
14. 14. Example  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!
15. 15. 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 Happy? You’ll actually get to use a calculator for these =]
16. 16. Try These: Both  Find the balance for each account. Amount Deposited: \$900, Annual Interest Rate: 2%, Time: 3 Years.  Compounding Annually  Compounding Semiannually
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