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# Compound Interest

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### Compound Interest

1. 2. What is compound interest? What is balance? Sum of the principal plus the interest earned Interest paid on the principal and on the interest accumulated to date. Used in savings accounts, credit cards Compounded for daily, quarterly (4 times a year) , semi-annually (twice a year), or annually Use the compound interest table
2. 3. Compound Interest Chart- shows what factor the deposit will be multiplied by to find the balance factor
3. 4. Let’s look at a problem: Ms. Johnson deposits \$12,000 in a savings account that pays interest quarterly. The annual interest rate paid by the bank is 6%. How much money will she have in the bank at the end of one year? 1. Find the interest rate per period: Number of interest periods- 4 (1 year has 4 quarters) Quarterly rate of interest- 6% ÷ 4 = 1.5% 2. Go to Interest table
4. 5. 3. Multiply the deposit by the factor to find the balance. 1.0614 x \$12,000 = \$12,736.80 4. Subtract the PRINCIPAL from the BALANCE to find how much interest is earned. \$12,736.80- 12,000 = \$736.80 So, Ms. Johnson will earn \$736.80 interest leading to a balance of \$12,736.80 at the end of the year.
5. 6. Here’s another: Mel deposits \$5000 in an account. The annual interest rate is 8%, compounded semi-annually. How much interest will he earn in 1 year? What is the balance after 1 year? <ul><li>Find the number of periods- semi-annually refers to 2 periods </li></ul><ul><li>Rate of interest- 8% ÷ 2 = 4% </li></ul>2. Look for the factor
6. 7. 3. Multiply the deposit by the factor. 1.0816 x \$5000 = \$5408 (BALANCE) 4. Subtract the principal from the balance. \$5408 – 5000 = \$408 (INTEREST EARNED) <ul><li>Find the number of interest periods and the rate of interest. </li></ul><ul><ul><li>Periods- 4 x 2 = 8 periods </li></ul></ul><ul><ul><li>Rate of interest- 8% ÷ 4 = 2% </li></ul></ul>2. Look for factor Let’s look at one more- multiple years: Dylan deposits \$4000 in his savings account. The annual interest rate is 8% compounded quarterly. How much interest will he earn in 2 years?
7. 8. 3. Multiply the deposit by the factor: 1.1717 x \$4000 = \$4686.80 (BALANCE) 4. Subtract the principal from the balance: \$4686.80 – 4000 = 686.80 (INTEREST EARNED)
8. 9. Now you will practice. \$10,000 deposit at an annual rate of 7% compounded semi-annually for 2 years 2. Use chart on page 200 1. 2 x 2 = 4 periods, 7% ÷ 2 = 3.5% 3. \$10,000 x 1.1475 = \$11,475 (BALANCE) 4. \$11,475 – 10,000 = \$1,475 (INTEREST EARNED)