## Investing for a Single Period

Suppose you invest $100 in a savings account that pays 10 percent interest per year. How much will you have in one year? You will have $110. This $110 is equal to your original principal of $100 plus $10 in interest that you earn. We say that $110 is the future value of $100 invested for one year at 10 percent, and we simply mean that $100 today is worth $110 in one year, given that 10 percent is the interest rate.

In general, if you invest for one period at an interest rate of r your investment will grow to (1 + r) per dollar invested. In our example, r is 10 percent, so your investment grows to 1 + .10 = 1.1 dollars per dollar invested. You invested $100 in this case, so you ended up with $100 X 1.10 = $110.

compounding

The process of accumulating interest on an investment over time to earn more interest.

interest on interest

Interest earned on the reinvestment of previous interest payments.

compound interest

Interest earned on both the initial principal and the interest reinvested from prior periods.

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