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# Section 11.3 Compound Interest

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1. Section 11.3Compound Interest

2. What You Will Learn • Compound Interest • Present Value

3. Investments • An investment is the use of money or capital for income or profit. In a fixed investment, the amount invested as principal is guaranteed and the interest is computed at a fixed rate. In avariable investment, neither the principal nor the the interest is guaranteed.

4. Compound Interest • Interest that is computed on the principal and any accumulated interest is called compound interest.

5. Compound Interest Formula A is the amount that accumulates in the account p is the principal r is the annual interest rate as a decimal t is the time in years n is the number of compound periods per year

6. Example 2: Using the Compound Interest Formula Kathy Mowers invested \$3000 in a savings account with an interest rate of 1.8% compounded monthly. If Kathy makes no other deposits into this account, determine the amount in the savings account after 2 years.

7. Example 2: Using the Compound Interest Formula Solution p = \$3000, r = 0.018, n =12, t = 2

8. Example 2: Using the Compound Interest Formula Solution The amount in the account after 2 years would be about \$3109.88.

9. Annual Percent Yield • The effective annualyieldor annual percentage yield (APY) is the simple interest rate that gives the same amount of interest as a compound rate over the same period of time.

10. Present Value Formula p is the present value, or principal to invest now A is the amount to be accumulated in the account r is the annual interest rate as a decimal n is the number of compound periods per year t is the time in years

11. Example 5: Savings for College • Will Hunting would like his daughter to attend college in 6 years when she finishes high school. Will would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter’s college expenses. If Will estimates that he will need \$30,000 in 6 years, how much should he invest now in a CD that has a rate of 2.5% compounded quarterly?

12. Example 5: Savings for College • Solution Will Hunting needs to invest approximately \$25,833.30 now to have \$30,000 in 6 years.