Continuous Compound Interest Word Problems Lesson

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. $$Pe^{rt}$$ $$1989e^{.03 \cdot 8}=\$2528.51$$

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