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Find the rate if a principal of $5,000 earned $1,350 interest in 6 years.

4.5%

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Find the rate if a principal of $9,000 earned $1,755 interest in 3 years.

6.5%

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Solve simple interest applications

Applications with simple interest    usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula.

We will start by solving a simple interest application to find the interest.

Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years?

Solution

We are asked to find the Interest, I .

Organize the given information in a list.

I = ? P = $12,500 r = 4% t = 5 years

Write the formula. I = P r t
Substitute the given information. I = ( 12,500 ) ( 0.04 ) ( 5 )
Simplify. I = 2,500
Check your answer. Is $2,500 a reasonable interest on $12,500 over 5 years?
At 4% interest per year, in 5 years the interest would be 20% of the principal. Is 20% of $12,500 equal to $2,500? Yes.
Write a complete sentence that answers the question. The interest is $2,500.
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Areli invested a principal of $950 in her bank account with interest rate 3%. How much interest did she earn in 5 years?

$142.50

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Susana invested a principal of $36,000 in her bank account with interest rate 6.5% . How much interest did she earn in 3 years?

$7,020

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There may be times when you know the amount of interest earned on a given principal    over a certain length of time, but you don't know the rate. For instance, this might happen when family members lend or borrow money among themselves instead of dealing with a bank. In the next example, we'll show how to solve for the rate.

Loren lent his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest. What was the rate of interest?

Solution

We are asked to find the rate of interest, r .

Organize the given information.

I = 660 P = $3,000 r = ? t = 4 years

Write the formula. I = P r t
Substitute the given information. 660 = ( 3,000 ) r ( 4 )
Multiply. 660 = ( 12,000 ) r
Divide. 660 12,000 = ( 12,000 ) r 12,000
Simplify. 0.055 = r
Change to percent form. 5.5% = r
Check your answer. Is 5.5% a reasonable interest rate to pay your brother?
I = P r t
660 = ? ( 3,000 ) ( 0.055 ) ( 4 )
660 = 660
Write a complete sentence that answers the question. The rate of interest was 5.5%.
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Jim lent his sister $5,000 to help her buy a house. In 3 years, she paid him the $5,000 , plus $900 interest. What was the rate of interest?

6%

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Hang borrowed $7,500 from her parents to pay her tuition. In 5 years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of interest?

4%

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There may be times when you take a loan for a large purchase and the amount of the principal is not clear. This might happen, for instance, in making a car purchase when the dealer adds the cost of a warranty to the price of the car. In the next example, we will solve a simple interest    application for the principal.

Eduardo noticed that his new car loan papers stated that with an interest rate of 7.5% , he would pay $6,596.25 in interest over 5 years. How much did he borrow to pay for his car?

Solution

We are asked to find the principal, P .

Organize the given information.

I = 6,596.25 P = ? r = 7.5% t = 5 years

Write the formula. I = P r t
Substitute the given information. 6,596.25 = P ( 0.075 ) ( 5 )
Multiply. 6,596.25 = 0.375 P
Divide. 6,596.25 0.375 = 0.375 P 0.375
Simplify. 17,590 = P
Check your answer. Is $17,590 a reasonable amount to borrow to buy a car?
I = P r t
6,596.25 = ? ( 17,590 ) ( 0.075 ) ( 5 )
6,596.25 = 6,596.25
Write a complete sentence that answers the question. The amount borrowed was $17,590.
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Practice Key Terms 4

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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