Formula for Calculating Continuous Interest

by Charlotte Johnson

One of the advantages of putting your money in various investment programs is acquiring interest on your principal. In some types of investment accounts, interest is being continuously compounded rather than calculated at yearly, quarterly or monthly intervals. Calculating continuous interest is based on a mathematical formula that involves the principal, the interest rate per year, and the number of years for which you are computing.

Beginning Data

The principal amount is the foundation for your calculation. For example, you may have invested \$30,000 in certificate of deposit. One of the first things most investors investigate when investing money is the interest rate. Consider an interest rate of 2.5 percent for this example. The higher the interest rate, the more money you will earn.

Examining a Time Period

Many investments offer higher interest rates for longer periods of investment. If you invest \$30,000 in an account that matures in one year, your interest rate may be much lower than if you invested the money for 10 years. For this example, assume that the interest rate is 2.5 percent for a period of two years.

Breaking Down the Formula

The mathematical formula for calculating continuous interest is A = Pe^rt. In this formula, A is the ending balance after a period of time. The variable P stands for principal. The variable e is a constant that represents a mathematical value known as Napier's constant. This value for any continuous interest equation equals approximately 2.7183. The variables r and t stand for annual interest rate and period of time, respectively.

Computing the Formula

Begin to work through the formula by converting the yearly interest rate on the account to a decimal by dividing by 100. In this example, you would divide 2.5 by 100 to get 0.025. Next multiply the interest rate in decimal form by the number of years for which you are calculating continuous interest. In this example, you would multiply two by 0.025 to get 0.05. Raise the number 2.7183 (the e in the formula) to the product of the interest rate times the time period. In this example, you would raise 2.7183 to the exponent 0.05 to get 1.0513. Multiply this value by the principal to find the ending balance. In this example, you would multiply 1.0513 by \$30,000 to get an ending balance of \$31,539.

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