Section 10.3 Compound Interest Investments that involve compound interest may play an important role in reaching some of your long-term financial goals.

Investments Compound Interest Investment: The use of money or capital for income or profit. Fixed Investment: The amount invested as principal is guaranteed and the interest is compounded at a fixed rate. Example. Savings account, money market deposit accounts Variable Investment: Neither the principal nor the interest is guaranteed. Ex. Stocks, mutual funds, and commercial bonds. Compound Interest Compound Interest: Interest that is compounded on the principal and any accumulated interest.

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: Using the Compound Interest Formula Kathy 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. After 2 years, what will the amount of interest be at 1.8% compounded monthly?

Example: Using the Compound Interest Formula Calculate the interest on $650 at 8% compounded semiannually for 3 years, using the compound interest formula.

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: Savings for College Will 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.

Annual Percent Yield Effective Annual Yield or (Annual Percentage Yield or APY): The simple interest rate that gives the same amount of interest as a compound rate over the same period of time. Many banks compound daily, so when computing the effective annual yield, they use 360 for the number of periods in a year. To determine the effective annual yield for any interest rate, calculate the amount using the compound interest formula where p is $1. Then subtract $1 from that amount. The difference written as a percent, is the effective annual yield. Example: Determine the annual percentage yield for $1 invested for 1 year at the following interest rates. a) 2% compounded quarterly b) 3% compounded monthly