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Chapter 11 Consumer Mathematics

WHAT YOU WILL LEARN • Compound Interest

Section 3 Compound Interest

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 a variable investment, neither the principal nor the the interest is guaranteed.

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

Example: Compound Interest Formula Mr. Martin put $5000 into a trust fund on his daughter’s 16th birthday. The trust fund pays 9% interest compounded semiannually. What will the trust fund be worth on her 21st birthday?

Solution The trust fund will be worth $7764.85 on her 21st birthday.

Annual Percent Yield The effective annual yield or 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.

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

EXAMPLE: Present Value Formula Jim Garrison wants to have $30,000 available in 3 years to buy a new car. How much does he need to invest now in a CD paying 5.25% interest compounded monthly?

Solution Jim Garrison needs to invest approximately $25,637.11 now to have $30,000 in 3 years for his new car.