Continuously Compounded Interest

Formula for Continuously Compounded Interest

To calculate continuously compounded interest use the formula below. In the formula, A represents the initial amount in the account

formula for how to calculate continuously compounded interest

Continuously Compounded Interest is a great thing when you are earning it! Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned!

Practice Problems

Problem 1

If you invest $1,000 at an annual interest rate of 5% compounded continuously, calculate the final amount you will have in the account after five years.

one thousand dollars compounded continuously at 5 percent interest

Problem 2

If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years.

500 hundred dollars compounded continuously at 10 percent interest

Problem 3

If you invest $2,000 at an annual interest rate of 13% compounded continuously, calculate the final amount you will have in the account after 20 years.

$$ A = Pe^{rt} \\ A = 2,000\cdot e^{.13 \cdot 20} \\ A = \boxed{ \$26,927.47} $$

Problem 4

If you invest $20,000 at an annual interest rate of 1% compounded continuously, calculate the final amount you will have in the account after 20 years.

500 hundred dollars compounded continuously at 10 percent interest

Problem 5

What is ... ?

Solution