Lesson Objectives
• Learn how to solve compound interest word problems

## How to Solve Compound Interest Word Problems

In this lesson, we want to talk about the compound interest formula. Earlier in the course, we looked at the simple interest formula, I = Prt, which tells us the simple interest earned based on a given principal or amount invested, the rate as a decimal, and time, usually in years. With simple interest, you won’t earn any interest on interest; the interest is just given on the initial principal or investment amount. Now with compound interest, you will earn interest on interest. So our formula for compound interest is really important to understand.

### 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
Let’s look at an example.
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. A 1.9% B 2% C 3% D 7% E 4% 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?

A
$12,825.42 B$14,245.32
C
$12,889.70 D$13,550.57
E
$12,755.21 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?

$5226 B$8,990
$2,113 D$6,158