Lesson Objectives
• Learn how to solve a word problem with the continuous compound interest formula

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

In the last lesson, we learned how to solve a word problem that involved the compound interest formula. For a given time period, as we increase the number of compounding periods or how often our interest is deposited in our account, the account balance gets larger, but only to a certain point. There is a maximum amount of interest that you can earn by increasing the number of compounding periods for a given time period and a given interest rate. Let's look at the formula for 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
Let's look at an example.
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. A$9,784.23
B
$9,447.70 C$8,172.47
D
$8,942.11 E$7,335.22

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. A$7,652.33
B
$5,108.38 C$4,328.77
D
$4,169.56 E$4,339.71

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. A$12,848.19
B
$11,169.68 C$11,979.57
D
$11,567.54 E$12,49.99         