- Learn how to solve compound interest word problems

## How to Solve Compound Interest Word Problems

### Compound Interest Formula

$$A=P\left(1+ \frac{r}{n}\right)^{tn}$$ Now the main thing for these word problems is to make sure you understand what each letter in the formula represents:- A is the future value or the account balance at the end of the investment period
- P is the principal, or amount invested, or the present value of the investment
- r is the interest rate as a decimal
- n is the number of compounding periods per year
- t is the number of years

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

Heather invests $7,717 in a savings account with a fixed annual interest rate of 8% compounded 2 times per year. What will the account balance be after 7 years?

Let's just fill out our variables and plug into our formula:

$$P=$7717$$ $$r=.08$$ $$n=2$$ $$t=7$$ $$A=7717\left(1 + \frac{.08}{2}\right)^{7 \cdot 2}$$ $$A=13{,}363.35$$

#### Skills Check:

Example #1

Solve each word problem.

Jack invests $1,116 in a savings account with a fixed annual interest rate compounded continuously. After 5 years, the balance reaches $1,363.09. What is the interest rate of the account?

Please choose the best answer.

Example #2

Solve each word problem.

Beth invests $7,818 in a savings account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 11 years?

Please choose the best answer.

Example #3

Solve each word problem.

Maggie invests a sum of money in a retirement account with a fixed annual interest rate of 5% compounded continuously. After 16 years, the balance reaches $13,704.88. What was the amount of the initial investment?

Please choose the best answer.

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