Compound Interest Word Problems Lesson

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

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