1. Big Idea Compound Interest is the way most banks and other savings institutions pay savers who put their money into their accounts. Repeated Multiplication Property of Powers When n is a positive integer, x = x  x  …  x. n factors { n

2. Warm-Up In the following table, P1, P2, and P3 stand for the three population estimates on page 397 and x stands for the number of years from now. Complete the table. Then discuss the results and describe trends in the data. x 1 2 10 60

3. Compound Interest Formula If a principal P earns an annual yield of r, then after t years there will be a total amount A, where A = P( 1 + r ) t

4. Additional Examples 1. Suppose you deposit P dollars in a savings account upon which the bank pays an annual yield of 3.5%. If the account is left alone, how much money will be in it at the end of a year? 2. Suppose you deposit $200 in a savings account upon which the bank pays an annual yield of 3.5%. a. If the account is left alone, how much money will be in it at the end of three years? b. How much interest did you earn in the three years?

5. Additional Example 3. When the twins were born, their parents put $3,000 into an account for college. What will be the total amount of money in the account after 19 years at an annual yield of 5.9%?

6. Most financial institutions compound interest on investments more than once a year. The formula for compound interest given in this lesson can be modified to take this into account. Explain to the students that if a financial institution compounds interest more often, the formula would be A = P ( 1 + r ) where n is the number of times interest n is compounded each year. nt What value of n would be used if it says annually, semi-annually, quarterly, and monthly? 1, 2, 4, 12 respectively.