##### 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.

Formula for Continuously Compounded Interest

To calculate continuously compounded interest use the formula below. In the formula, A represents the final amount in the account that starts with an initial (principal) P using interest rate r for t years. This formula makes use of the mathemetical constant e .

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!

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.

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.

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.

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.