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

A continuously compounding CD can help you grow your money.

A continuously compounding CD can help you grow your money.

A certificate of deposit (CD) is one of the safest places to park your cash, and typically offers a higher interest rate than a regular savings account. Most CDs earn compound interest, which means you earn interest on your initial investment and on previously earned interest. A CD can compound, or calculate interest, daily, monthly or at some other interval. With continuous compounding -- the most frequent compounding available -- you earn interest 24/7. With all else being equal, you earn more interest on a CD that compounds continuously than on one that compounds at a less-frequent interval.

Multiply the CD’s annual interest rate as a decimal by the number of years until it matures. For example, assume you want to know how much interest you will earn on a two-year $5,000 CD that pays 7 percent annual interest compounded at a continuous rate. Multiply 2 by 0.07 to get 0.14.

Raise Euler's number, “e,” to the power of your Step 1 result. Euler's number equals approximately 2.7182818. You can substitute this number for “e” if your calculator lacks an “e” function. In this example, raise “e” to the 0.14 power to get 1.150274.

Multiply your result by your initial investment in the CD to determine its value when it matures. In this example, multiply $5,000 by 1.150274 to get $5,751.37. This means your CD will grow to $5,751.37 at the end of two years after earning continuously compounded interest.

Subtract your initial investment from your result to calculate the amount of interest earned. Concluding the example, subtract $5,000 from $5,751.37 to get $751.37 in interest earned from continuous compounding.


  • Although continuous compounding earns the most interest compared to other compounding intervals, daily compounding comes in at a close second. The difference between interest earned on a continuously compounded CD and that on a daily compounded CD is negligible.


  • If you withdraw money from your CD before its maturity, you’ll reduce the effects of continuous compounding and might be responsible for early-withdrawal penalties.

About the Author

Bryan Keythman has performed stock investment research and writing for a consulting firm since 2008. He also has prior experience sourcing and underwriting commercial real-estate investment and development opportunities for a commercial real-estate developer. Keythman holds a Bachelor of Science in finance.

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