How to Calculate the Interest on a Certificate of Deposit with a Continuous Rate

by Mark Kennan

A certificate of deposit, or CD for short, is a bank deposit account that pays you a preset rate of interest in return for leaving the money in the account for a predetermined period of time. Typically, the more money you put in and the longer you agree to leave it in the CD, the higher your interest rate. Continuous compounding refers to having the interest added to the account as soon as it accrues, which increases your return because you have more money in your account to earn interest.

Divide the annual interest rate expressed as a percentage by 100 to convert it to an annual interest rate expressed as a decimal. For example, if the CD pays 3.3 percent per year, divide 3.3 by 100 to get 0.033.

Multiply the interest rate by the number of years the money remains in the account. For example, if the annual interest rate equals 3.3 percent and the CD has a term of 3 years, multiply 0.033 by 3 to get 0.099.

Raise e, Napier's number, or the base of the natural logarithm, to the power of the Step 2 result. Napier's number is approximately 2.7183. In this example, raise 2.7183 to the 0.099th power to get 1.10406703.

Multiply the result of Step 3 by the beginning balance of the certificate of deposit to find the maturity value of the certificate of deposit. In this example, if your CD started with a balance of $4,920, multiply $4,920 by 1.10406703 to find that the maturity value equals $5,432.01.

Subtract the beginning value of your CD from the maturity value of the CD to find the interest on the CD. Finishing the example, subtract $4,920 from $5,432.01 to find $512.01 in interest accumulated.

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