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8.21: Simple Interest

Difficulty Level: Basic Created by: CK-12
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Have you ever needed to take a loan to make a large purchase? Kevin is looking at doing just that.

Kevin has been gotten a job at the supermarket. He knows that over the next few months he will make enough money to purchase a new bike. The bike that Kevin is interested in costs $300.00. The man at the bike store told Kevin that he could get a loan for the bike with 2% annual interest.

If it takes Kevin 3 years to pay off the loan, how much interest will he have to pay?

This Concept will teach you how to calculate simple interest. At the end, you will know how to figure out this amount.

Guidance

Interest is another amount that is ADDED to a total. You hear the word “interest” when talking about borrowing money. When someone borrows money from the bank, the bank charges them a small percent of the amount that the person borrowed for each period of time that they have the money. The percent is often calculated annually or per year. In this way, the bank says, “We will loan you this money, but until you pay it back, you must pay us for each month or year that you have it.”

How can we calculate interest?

There are three main things that you need to know to calculate interest. You need to know the amount that was borrowed or the principal , the rate or the percentage the bank is charging to loan the money, and the time that you are keeping the money.

Here is a formula we can use to calculate interest.

I &= prt\\Interest &= principal \times rate \times time

We take the principal, multiply it with the rate, and multiply that with the length of time that the money has been borrowed, to find the interest.

Carrie borrowed $500.00 from the bank. The bank charges 5% interest annually. If it takes Carrie 1 year to pay back the money, how much interest will she pay?

To figure this out, let’s use our formula.

I = prt

The principal is $500.00.

The rate is 5% = .05

The time is 1 year.

& I=(500)(.05)(1)\\\\& \qquad \quad \;500\\& \qquad \underline{\times \ \ .05}\\& \qquad \ 25.00

Carrie will pay $25.00 in interest.

What if it had been 3 years before she had paid back the money? If this was the case, we would have used this formula.

I &= (500)(.05)(3)\\I &= (25.00)(3)\\I &= \$75.00

Carrie would have paid $75.00 in interest.

Try a few of these on your own.

Example A

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

Solution: $30.00

Example B

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

Solution: $12.00

Example C

Carmen has $1200.00 in her savings account at 3% interest. In three years, how much interest will she accrue?

Solution: $72.00

Now back to the original problem once again.

Kevin has been gotten a job at the supermarket. He knows that over the next few months he will make enough money to purchase a new bike. The bike that Kevin is interested in costs $300.00. The man at the bike store told Kevin that he could get a loan for the bike with 2% annual interest.

If it takes Kevin 3 years to pay off the loan, how much interest will he have to pay?

To calculate the interest, we can use the formula that was introduced in the Concept.

I = prt

Next, we substitute in the given values.

I = (300)(.02)(3)

I = 18

Kevin will pay $18.00 in interest.

Vocabulary

Here are the vocabulary words in this Concept.

Percent
a part of a whole 100, written using a % sign.
Interest
the sum of money a person pays a bank for borrowing money
Principal
the amount of money borrowed
Rate
a percent that the bank charges for borrowing money
Annually
per year

Guided Practice

Here is one for you to try on your own.

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 accrue?

Answer

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

I = prt

I = (2500)(3.5)(4)

I = 350

Kelly's account will accrue $350.00 in interest.

Video Review

Here is a video for review.

Khan Academy: Introduction to 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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Difficulty Level:

Basic

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Date Created:

Oct 29, 2012

Last Modified:

Aug 19, 2014
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