Solve Real-World Problems
Involving Simple Interest
Jen Kershaw
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Printed: October 15, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Solve Real-World Problems Involving Simple Interest
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Solve Real-World Problems
Involving Simple Interest
Here you’ll solve real-world problems involving simple interest.
Have you ever tried to figure out a problem involving interest? Take a look at this dilemma.
With a goal of boosting student attendance at football games, the student council has decided to invest a portion of
their savings for middle school decorations. They figure that when the games are happening that they can decorate
the middle school with balloons, banners and flyers.
“I think it will help make it a priority for students,” Jeremy said at the weekly student council meeting.
“It will be a lot of fun too. We could even host a pep rally to help get the kids charged up,” Candice suggested.
“We put $4000 in the bank in the sixth grade. Now that we are 8th graders that money has been sitting in the bank
for two years at a 4% interest rate,” Jeremy explained.
Candice began working out the math in her head. If they did put $4000 in the bank for two years and they had a 4%
interest rate, then there definitely is more money in there now. She began to complete the calculations in her head.
Do you have an idea how to figure this out? This problem involves principal, interest rates and time. This
Concept will teach you all about calculating simple interest. Pay close attention and you will see this problem
again at the end of the Concept.
Guidance
Money is a necessary part of everyday life, and as you get older, your relationship to money will change. In this
lesson, we will explore some of the ways in which you will relate to money as you get older.
Saving money and making wise investments will be an important part of your financial planning. Part of making
investing is earning interest. When you save money in the bank, the bank uses that money for its own investments. In return for using your money, the bank pays you a certain percent. This percent is your interest .
Interest is the percent that a bank pays you for using keeping your money in their bank.
Banks compete with each other for your money because they want you to put your money in their bank. They try to
give you the best “interest rate” that they can. This means that they will pay you a greater percentage than another
bank to try to get your business. The greater the interest rate that they pay you; the more likely you are to invest
your money with them in a savings account. The more money you save, the more they have to invest. They publish
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an interest rate r which tells you what percent they will pay you per year t. The principal, p is the amount of
money that you have put into the bank.
You can use this information in the formula I = prt in order to calculate the interest that you will earn on your
principal p.
Take a few minutes and write this formula in your notebook.
Now let’s look at how we can use this formula to calculate interest.
You invest $5,000 in a bank for 2 years at a 4% interest rate. What is the interest you have earned after this time?
We start by looking at the given information. Then use the formula to calculate interest.
p = 5000, r = .04,t = 2.
Use the formula to calculate interest.
I = prt
I = 5000 · .04 · 2
I = 400
The bank will pay you $400 in interest over two years at that rate.
Many investors may have specific goals—they want to earn a certain amount of interest on their investments. Because
of this, they need to figure out the time that it takes to earn a certain amount of money. The formula I = prt is an
equation. We can use the Multiplication Property of Equations to solve for t if we know I, r, and p.
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Chapter 1. Solve Real-World Problems Involving Simple Interest
Mrs. Duarte has $20,000 to invest. She wants to earn $10,000 in interest. She is considering a savings and loans
bank that is offering her 5.6% interest per year. For how long will she have to leave her money in the bank in order
to reach her goal of $10,000?
Start by looking at the given information.
I = 10000, p = 20000, r = .056 Solve for t.
Next, we substitute the given values into the formula and solve the equation.
I = prt
10000 = 20000 · .056 · t
10000 = 1120t
10000 1120t
=
1120
1120
8.93 = t
She will have to leave her money in the bank for nearly 9 years.
Exactly! We are using what we have learned about solving equations to figure out missing information
regarding interest and banking.You can use the simple interest formula I = prt to find any of the missing variables
if you are given values of the others. We have used it to solve for I and t. Of course, once the bank pays you
interest, your account balance grows. You start of with your principal p and then you add your interest I.
Now let’s see how much a bank balance would be after a given time at a given interest rate.
Jessica invests $3,000 in a credit union at an interest rate of 3.9%. She leaves the money there for 5 years. What is
her balance after that time?
To answer this question, we will need to do two things. First, we will need to figure out the amount of the
interest. Then we can add this amount to the principal that Jessica first invested. This will give us the new
balance.
First find the interest that she earned:
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p = 3000, r = .039,t = 5
I = prt
I = 3000 · .039 · 5
I = 585
She earned $585 in interest. Her principal was $3,000. How much does she have now?
585 + 3000 = 3585
She has $3,585. This is the new balance.
Solve each problem.
Example A
An investor places $15,000 in a savings account that pays 4.5% interest. She will leave the money there for 6 years.
What will her interest be?
Solution: Her interest after 6 years will be $4,050.
Example B
A bank is offering an interest rate of 4.75%. How long would it take to earn $500 if you invested $12,000 in the
bank?
Solution: It would take .88 years or about 10 12 months.
Example C
If you charge $7,000 on a credit card and you bank charges you 15.9%, how much would you owe after a year?
Solution: You would owe $8,113.
Now let’s go back to the dilemma from the beginning of the Concept.
Now we need to figure out the interest and the final balance in the student council bank account.
First, let’s find the amount of the interest.
I = PRT
I = (4000)(.04)(2)
I = $320.00
Next, we add this to the original amount invested.
$4000 + $320 = $4320.00
This is the new balance in the student council account.
Vocabulary
Interest
The amount of money paid or owed after a period of time. It is based on a percentage.
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Chapter 1. Solve Real-World Problems Involving Simple Interest
Rate
The percent charged or paid by a bank given a savings account or a loan amount.
Principal
The amount of the original loan or original deposit.
Guided Practice
Here is one for you to try on your own.
A nurse put $22,000 in the bank 15 years ago. She has earned $21,450 in interest—nearly as much as her initial
investment. What was the interest rate that the bank was paying her?
Solution
Using the simple interest formula I = prt, we can calculate the interest rate r if we are given the I, p and t values.
As before, we will substitute the known values and then use inverse operations to find the missing value.
I = 21450, p = 22000,t = 15
I = prt
21450 = 22000 · r · 15
21450 = 330000r
21450
330000r
=
330000
330000
.065 = r
Because we are looking for a percent-an interest rate, we have to change the decimal to a percent.
.065 = 6.5%
The bank was paying 6.5%.
Video Review
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5523
Simple Interest
Explore More
Directions: Use the simple interest formula I = prt to solve for the Interest.
1. Find I if p = 62, 300, r = .0525,t = 14.
2. Find I if p = 9800, r = .028,t = 9.
3. Find I if p = $600, r = .05,t = 8
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4.
5.
6.
7.
8.
9.
10.
Find I
Find I
Find I
Find I
Find I
Find I
Find I
if
if
if
if
if
if
if
p = $2300, r = .06,t = 12
p = $5500, r = .08,t = 7
p = $400, r = .05 and t = 5
p = $700, r = .03 and t = 9
p = $500, r = .06 and t = 12
p = $800, r = .09 and t = 7
p = $950, r = .06 and t = 4
Directions: Find the new interest and then find the new balance with the given information. There are two steps to
solving these problems.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
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p = 43000, r = .0365,t = 11
p = 7000, r = .079,t = 4
p = 8000, r = .06,t = 3
p = 18000, r = .04,t = 5
p = 25000, r = .05,t = 3
p = 3000, r = .05,t = 7
p = 12000, r = .04,t = 5
p = 9000, r = .06,t = 10
p = 7500, r = .03,t = 8
p = 27500, r = .04,t = 6