The formula for compound annual growth is typically used to determine the future value of an account after taking into consideration compound interest. However, with slight modifications, you can use it to figure out the original principal of an account based on the ending balance, interest rate and time. When figuring the time, you need to know the number of times each year the interest compounds. This is because accounts that compound interest more frequently accrue interest at a faster rate. Calculating the original amount helps you determine how much money you need to start with to reach your investing goals.
1. Divide the interest rate by 100 to convert to a decimal. For example, if your account pays a quarterly interest rate of 1.35 percent, divide 1.35 by 100 to get 0.0135.
2. Add 1 to the periodic interest rate of your account. In this example, add 1 to the quarterly interest rate of 0.0135 to get 1.0135.
3. Raise the result to the N power, with N equaling the number of times interest compounds on your account. For this example, because interest compounds four times per year, if the interest accumulated over 4.25 years, this means the interest accumulated over 17 compounding periods. Raise 1.0135 to a power of 17 to get 1.256040958.
4. Divide the ending balance by the result to find the original principal in the account. Completing the example from the previous step, if you ended with $31,000 in the account, divide $31,000 by 1.256040958 to find the original principal equals about $24,680.72.
- Comstock/Comstock/Getty Images