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- 1. Simple and Compound Interest
- 2. Warm Up: Find 6% of $400. Find 5% of $2,000. Find 4.5% of $700. Find 5.5% of $325.
- 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. Simple Interest Formula I = prt I = interest P = principal R = the interest rate per year T = the time in years.
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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