- Learn how to solve a word problem with the continuous compound interest formula

## How to Solve a Word Problem with Continuous Compound Interest

### Continuous Compound Interest Formula

$$Pe^{rt}$$- P is the amount invested or the principal
- e is a special number known as Euler's number
- r is the rate as a decimal
- t is the time in years

Example #1: Solve each word problem. Round your answer to the nearest hundredth.

Mia invests $1,989 in a savings account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 8 years?

We only need to plug into our formula. Here, our principal is $1,989, our rate is .03, and our time is 8. $$Pe^{rt}$$ $$1989e^{.03 \cdot 8}=\$2528.51$$

#### Skills Check:

Example #1

Solve each word problem.

Molly invests $5,211 in a retirement account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 18 years?

Please choose the best answer.

Example #2

Solve each word problem.

Rob invests $2,909 in a savings account with a fixed annual interest rate of 4% compounded continuously. What will the account balance be after 9 years?

Please choose the best answer.

Example #3

Solve each word problem.

Claire invests $7,339 in a savings account with a fixed annual interest rate of 7% compounded continuously. What will the account balance be after 6 years?

Please choose the best answer.

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