How to Compute a Compound Interest Rate

Determining compound interest takes some simple math.

In finance, compound interest is interest that builds up over time. Banks use compounding formulas when calculating the interest that accumulates on loans and savings account balances. For example, the longer you take to pay back a loan, the more interest you owe, and the longer you leave money in a savings account, the more interest you earn. Compound interest is different from simple interest, which is a one-time payment. To compute a compound interest rate, you need to know the annual interest rate, the principal and the period.

Things You'll Need

• Calculator

Instructions

1. Express the annual interest rate, R, as a decimal and add 1 to it. This new number is the annual growth factor. For example, if the annual interest rate on a savings account is 3 percent, add 0.03 and 1 to obtain 1.03. The formula for the annual growth factor is 1+R/100.

2. Compute the annual growth factor raised to the number of years the money is in the savings account, N. This is the total growth factor. For example, if you leave money in the account for five years, the total growth factor is 1.03^5 = 1.159274. The formula for the total growth factor is (1+R/100)^N.

3. Multiply the account principal, P, by the total growth factor. This is the total amount of money in the account after N years. For example, if you start with $1,000, after five years you will have ($1,000) times (1.159274) = $1,159.27 in the savings account. The general formula is P(1+R/100)^N.

4. Subtract the principal from the total amount of money to find the total amount of compound interest accrued. For example, the total interest earned in five years is $1,159.27 - $1,000 = $159.27. The general formula is P(1+R/100)^N - P.

References

• Math Reference Tables: Interest and Exponential Growth