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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. IInterest=prt=principal×rate×time\begin{align*}I &= prt\\ Interest &= principal \times rate \times time\end{align*} 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 borrowed500.00 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\begin{align*}I = prt\end{align*}

The principal is 500.00. The rate is 5% =.05\begin{align*}= .05\end{align*} The time is 1 year. I=(500)(.05)(1)500× .05 25.00\begin{align*}& I=(500)(.05)(1)\\ \\ & \qquad \quad \;500\\ & \qquad \underline{\times \ \ .05}\\ & \qquad \ 25.00\end{align*} Carrie will pay25.00 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.

III=(500)(.05)(3)=(25.00)(3)=75.00\begin{align*}I &= (500)(.05)(3)\\ I &= (25.00)(3)\\ I &= \75.00\end{align*} Carrie would have paid75.00 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\begin{align*}I = prt\end{align*} Next, we substitute in the given values. I=(300)(.02)(3)\begin{align*}I = (300)(.02)(3)\end{align*} I=18\begin{align*}I = 18\end{align*} Kevin will pay18.00 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\begin{align*}I = prt\end{align*} I=(2500)(3.5)(4)\begin{align*}I = (2500)(3.5)(4)\end{align*} I=350\begin{align*}I = 350\end{align*} Kelly's account will accrue350.00 in interest.

### Video Review

Here is a video for review.

### 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

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

Annually

An event occurs annually if it happens once per year.

Compound interest

Compound interest refers to interest earned on the total amount at the time it is compounded, including previously earned interest.

future value

In the context of earning interest, future value stands for the amount in the account at some future time $t$.

Percent

Percent means out of 100. It is a quantity written with a % sign.

present value

In the context of earning interest, present value stands for the amount in the account at time 0.

Simple Interest

Simple interest is interest calculated on the original principal only. It is calculated by finding the product of the the principal, the rate, and the time.

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