# 6.20: Simple Interest Equation to Find Interest Rate

**At Grade**Created by: CK-12

Have you ever borrowed money? Look at this dilemma.

While shopping at the candy store, a woman began complaining about paying interest on a loan. She said that she had paid $450.00 over 2 years after borrowing $2500. Taylor listened and thought about this dilemma.

Using the given information, can you figure out the interest rate?

**This Concept will teach you how to do this. We'll revisit this problem at the end of the Concept.**

### Guidance

This Concept is all about borrowing money, paying money back and the fees associated with borrowing money. This is where you will learn all about interest.

**What is interest?**

*Interest***is a charge for money that is borrowed.** When you borrow money, you pay the lender interest for borrowing the money. When you deposit money into a saving account at a bank, the bank pays you interest since the bank is borrowing money from you. So interest can be something that you have to pay or that is paid to you.

**The amount of money that is invested or borrowed is called the** ** principal.** If you borrow $500.00 this is the principal. It is the initial amount before any interest is added on.

**The** *rate of interest***is the percent charged or earned. We also have to consider the time in years that the money is borrowed or deposited when computing interest.**

**How do we calculate interest?**

We can calculate interest by using an equation. Here is the equation.

\begin{align*}\text{Interest} & = \text{Principal} \times \text{rate} \times \text{time}\\ I & = Prt\end{align*}

*Take a few minutes to write this equation down in your notebook.*

**If you know the amount of interest, the principal, and the time in years, you can find the interest rate.**

If you deposit $2,000 at USA Savings Bank, at the end of 2 years you will have received $240 in simple interest. What is the interest rate at USA Savings Bank?

\begin{align*}&I = Prt\\ &\$ 240 = \$ 2,000 \times r \times 2 \qquad \ \leftarrow \text{Substitute values.}\\ &\$ 240 = \$ 4,000 \times r \qquad \qquad \leftarrow \text{Simplify.}\\ &0.06 = r \qquad \qquad \qquad \qquad \ \leftarrow \text{Solve for}\ r.\end{align*}

Change 0.06 to the percent 6%.

**The interest rate is 6%.**

If you borrow $3,600 from USA Savings Bank for 18 months, at the end of the 18 months you will repay $4,059 to the bank. What is the interest rate for this loan?

**The amount to be repaid includes the principal plus the interest. Subtract the principal from the amount to be repaid to find the amount of the interest.**

\begin{align*}\$ 4,059 - \$ 3,600 = \$ 459\end{align*}

Since there are 12 months in a year, 18 months is \begin{align*}\frac{18}{12}\end{align*} or \begin{align*}1 \frac{1}{2}\end{align*} years.

\begin{align*}&I = Prt\\ &\$ 459 = \$ 3,600 \times r \times 1 \frac{1}{2} \qquad \ \leftarrow \text{Substitute values.}\\ &\$ 459 = \$ 5,400 \times r \qquad \qquad \ \ \leftarrow \text{Simplify.}\\ &0.085 = r \qquad \qquad \qquad \qquad \ \ \leftarrow \text{Solve for}\ r.\end{align*}

Change 0.085 to the percent 8.5%.

**The interest rate is 8.5%.**

Find the interest rate for each problem.

#### Example A

Jesse borrowed $500.00. At the end of the year he paid back $50.00 in interest. What was the interest rate?

**Solution:\begin{align*}10%\end{align*}**

#### Example B

Karen earned $200.00 in two years of simple interest on her initial investment of $400.00. What was the interest rate?

**Solution:\begin{align*}25%\end{align*}**

#### Example C

principal: $5,600; time: 9 months; simple interest: $357

**Solution:\begin{align*}8.5%\end{align*}**

Here is the original problem once again.

While shopping at the candy store, a woman began complaining about paying interest on a loan. She said that she had paid $450.00 over 2 years after borrowing $2500. Taylor listened and thought about this dilemma.

Using the given information, can you figure out the interest rate?

To figure this out, let's use the formula for finding simple interest.

\begin{align*}I = PRT\end{align*}

Now fill in the given information.

\begin{align*}450 = 2500(2)r\end{align*}

Next, we multiply.

\begin{align*}450 = 5000r\end{align*}

\begin{align*}\frac{450}{5000} = r\end{align*}

\begin{align*}r = .09 = 9%\end{align*}

**The woman has an interest rate of \begin{align*} 9%.\end{align*}**

### Vocabulary

Here are the vocabulary words in this Concept.

- Interest
- the amount of money added to a loan or to a deposit based on an initial loan or investment and an interest rate.

- Principal
- the original amount of money borrowed or invested

- Interest Rate
- the percent that is being given for an investment or for a loan. It depends on the amount of time the money is invested or borrowed.

### Guided Practice

Here is one for you to try on your own.

Wanda borrowed $5,000.00 from the bank. At the end of three years, she had paid $450.00 in interest. What is Wanda's interest rate?

**Answer**

To figure this out, we can use the formula for finding simple interest.

\begin{align*}I = PRT\end{align*}

Next, we fill in what we know.

\begin{align*}450 = 5000(3)r\end{align*}

We are trying to figure out the rate, so that is our variable.

\begin{align*}450 = 15000r\end{align*}

\begin{align*}\frac{450}{15000} = .03\end{align*}

**The interest rate was 3%.**

### Video Review

Here is a video for review.

- This is a James Sousa video on calculating simple interest.

### Practice

Directions: Find the simple interest on each amount.

1. $500.00 at 4% for 2 years

2. $200.00 at 5% for 3 years

3. $5000.00 at 2% for 2 years

4. $600.00 at 10% for 1 year

5. $1200.00 at 4% for 2 years

6. $1500.00 at 3% for 1 year

7. $2300.00 at 2% for 2 years

8. $500.00 at 4% for 2 years

9. $2500.00 at 5% for 5 years

10. $1500.00 at 11% for 2 years

11. $3500 at 3% for 5 years

12. $3500 at 4% for 15 years

13. $13,000 at 4.5% for 6 years

14. $23,000 at 3.5% for 10 years

15. $50,000 at 2.5% for 20 years

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Here you'll learn to use the simple interest equation to find an interest rate.

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