Kevin has just moved to a new city for a job. He needs furniture but doesn’t have enough money to buy everything he needs. The furniture salesman offers Kevin a store credit card. He can put the cost of the furniture on the card and pay it off over time. The interest rate on the card is 15%. Kevin buys $3,000 worth of furniture and puts it on the credit card. How much interest will Kevin pay if it takes him 3 years to pay off the balance?

In this concept, you will learn to calculate the simple interest on a loan.

### Calculating Simple Interest

Banks lend people money in the form of a loan. In return, the banks collect interest. **Interest** is the amount of money paid for the use of borrowed money. It is important to calculate the interest before taking a loan.

One way is with simple interest. **Simple interest** is a quick way to calculate the interest of a loan. The formula for simple interest is:

The **principal** is the sum of money being borrowed. **Interest rate** is the percent of the principal you pay in addition to the principal over a time period. Interest rates are usually calculated annually, or per year. **Time** is the amount of time the borrower has agreed to pay back the loan.

Let's look at an example.

Carrie borrowed $500 from the bank. The bank charges a 5% interest rate annually. If it takes Carrie 1 year to pay back the money, how much interest will she pay?

The principal is $500.

The rate is 5% per year or 0.05.

The time is 1 year.

Let’s use the formula for simple interest.

Carrie will pay $25.00 in interest.

Calculate the interest had it taken Carrie 3 years to pay back the loan.

Carrie would have paid $75.00 in interest.

### Examples

#### Example 1

Earlier, you were given a problem about Kevin’s furniture loan.

Kevin bought $3,000 worth of furniture and put it on a credit card with a 15% interest rate. He takes 3 years to pay off the loan. To calculate the interest, use the formula: \begin{align*}I = prt\end{align*}

Substitute in the given values.

Kevin will pay $1,350 in interest.

#### Example 2

Find the simple interest of the loan.

Kelly saved $2500.00 in her savings account. Her annual interest rate was 3.5%. In four years, how much interest will Kelly’s account accumulate?

The principal is $2500.

The rate is 3.5% per year or 0.035.

The time is 4 years.

Use the formula for simple interest.

Kelly’s account will accumulate $350.00 in interest.

#### Example 3

Mark borrowed $250.00 at 4% for 3 years. How much interest did he pay?

Use the formula for simple interest.

Mark will pay $30 in interest.

#### Example 4

Kris borrowed $300.00 at 2% for 2 years. How much interest did he pay?

Use the formula for simple interest.

Kris will pay $12 in interest.

#### Example 5

Carmen has $1,200.00 in her savings account at 3% interest. In two years, how much interest will she accumulate?

Use the formula for simple interest.

Carmen will pay $72 in interest.

### Review

Find the simple interest on each amount.

- $500.00 at 4% for 2 years
- $200.00 at 5% for 3 years
- $5000.00 at 2% for 2 years
- $600.00 at 10% for 1 year
- $1200.00 at 4% for 2 years
- $1500.00 at 3% for 1 year
- $2300.00 at 2% for 2 years
- $500.00 at 4% for 2 years
- $2500.00 at 5% for 5 years
- $1500.00 at 11% for 2 years
- $3500 at 3% for 5 years
- $3500 at 4% for 15 years
- $13,000 at 4.5% for 6 years
- $23,000 at 3.5% for 10 years
- $50,000 at 2.5% for 20 years

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.21.