6.5: Solve Simple Interest Applications
- Page ID
- 114927
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- Use the simple interest formula
- Solve simple interest applications
Be Prepared 6.9
Before you get started, take this readiness quiz.
Solve
If you missed this problem, review Example 5.43.
Be Prepared 6.10
Solve
If you missed this problem, review Example 5.44.
Use the Simple Interest Formula
Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal, and the bank pays you interest, The interest is computed as a certain percent of the principal; called the rate of interest, The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, represents the number of years the money is left in the account.
Simple Interest
If an amount of money, the principal, is invested for a period of years at an annual interest rate the amount of interest, earned is
where
Interest earned according to this formula is called simple interest.
The formula we use to calculate simple interest is To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.
Example 6.33
Find the simple interest earned after years on at an interest rate of
- Answer
Organize the given information in a list.
We will use the simple interest formula to find the interest.
Write the formula. Substitute the given information. Remember to write the percent in decimal form. Simplify. Check your answer. Is $90 a reasonable interest earned on $500 in 3 years? In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable. Write a complete sentence that answers the question. The simple interest is $90.
Try It 6.65
Find the simple interest earned after years on at an interest rate of
Try It 6.66
Find the simple interest earned after years on at an interest rate of
In the next example, we will use the simple interest formula to find the principal.
Example 6.34
Find the principal invested if interest was earned in years at an interest rate of
- Answer
Organize the given information in a list.
We will use the simple interest formula to find the principal.
Write the formula. Substitute the given information. Divide. Simplify. Check your answer. Is it reasonable that $2,225 would earn $178 in 2 years? Write a complete sentence that answers the question. The principal is $2,225.
Try It 6.67
Find the principal invested if interest was earned in years at an interest rate of
Try It 6.68
Find the principal invested if interest was earned in years at an interest rate of
Now we will solve for the rate of interest.
Example 6.35
Find the rate if a principal of earned interest in years.
- Answer
Organize the given information.
We will use the simple interest formula to find the rate.
Write the formula. Substitute the given information. Multiply. Divide. Simplify. Write as a percent. Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years? Write a complete sentence that answers the question. The rate was 11.5%.
Try It 6.69
Find the rate if a principal of earned interest in years.
Try It 6.70
Find the rate if a principal of earned interest in years.
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.
Example 6.36
Nathaly deposited in her bank account where it will earn interest. How much interest will Nathaly earn in years?
- Answer
We are asked to find the Interest,
Organize the given information in a list.
Write the formula. Substitute the given information. Simplify. 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.
Try It 6.71
Areli invested a principal of in her bank account with interest rate How much interest did she earn in years?
Try It 6.72
Susana invested a principal of in her bank account with interest rate How much interest did she earn in years?
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.
Example 6.37
Loren lent his brother to help him buy a car. In his brother paid him back the plus in interest. What was the rate of interest?
- Answer
We are asked to find the rate of interest,
Organize the given information.
Write the formula. Substitute the given information. Multiply. Divide. Simplify. Change to percent form. Check your answer. Is 5.5% a reasonable interest rate to pay your brother? Write a complete sentence that answers the question. The rate of interest was 5.5%.
Try It 6.73
Jim lent his sister to help her buy a house. In years, she paid him the plus interest. What was the rate of interest?
Try It 6.74
Hang borrowed from her parents to pay her tuition. In years, she paid them interest in addition to the she borrowed. What was the rate of interest?
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.
Example 6.38
Eduardo noticed that his new car loan papers stated that with an interest rate of he would pay in interest over years. How much did he borrow to pay for his car?
- Answer
We are asked to find the principal,
Organize the given information.
Write the formula. Substitute the given information. Multiply. Divide. Simplify. Check your answer. Is $17,590 a reasonable amount to borrow to buy a car? Write a complete sentence that answers the question. The amount borrowed was $17,590.
Try It 6.75
Sean's new car loan statement said he would pay in interest from an interest rate of over years. How much did he borrow to buy his new car?
Try It 6.76
In years, Gloria's bank account earned interest at How much had she deposited in the account?
In the simple interest formula, the rate of interest is given as an annual rate, the rate for one year. So the units of time must be in years. If the time is given in months, we convert it to years.
Example 6.39
Caroline got as graduation gifts and invested it in a certificate of deposit that earned interest. How much interest did this investment earn?
- Answer
We are asked to find the interest,
Organize the given information.
Write the formula. Substitute the given information, converting 10 months to of a year. Multiply. Check your answer. Is $15.75 a reasonable amount of interest? If Caroline had invested the $900 for a full year at 2% interest, the amount of interest would have been $18. Yes, $15.75 is reasonable. Write a complete sentence that answers the question. The interest earned was $15.75.
Try It 6.77
Adriana invested for months in an account that paid interest. How much interest did she earn?
Try It 6.78
Milton invested for months in an account that paid interest How much interest did he earn?
Section 6.4 Exercises
Practice Makes Perfect
Use the Simple Interest Formula
In the following exercises, use the simple interest formula to fill in the missing information.
Interest | Principal | Rate | Time (years) |
---|---|---|---|
Interest | Principal | Rate | Time (years) |
---|---|---|---|
Interest | Principal | Rate | Time (years) |
---|---|---|---|
Interest | Principal | Rate | Time (years) |
---|---|---|---|
Interest | Principal | Rate | Time (years) |
---|---|---|---|
Interest | Principal | Rate | Time (years) |
---|---|---|---|
In the following exercises, solve the problem using the simple interest formula.
Find the simple interest earned after years on at an interest rate of
Find the simple interest earned after years on at an interest rate of
Find the simple interest earned after years on at an interest rate of
Find the simple interest earned after years on at an interest rate of
Find the simple interest earned after years on at an interest rate of
Find the simple interest earned after years on at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the rate if a principal of earned interest in years.
Find the rate if a principal of earned interest in years.
Find the rate if a principal of earned interest in years.
Find the rate if a principal of earned interest in years.
Solve Simple Interest Applications
In the following exercises, solve the problem using the simple interest formula.
Casey deposited in a bank account with interest rate How much interest was earned in years?
Terrence deposited in a bank account with interest rate How much interest was earned in years?
Robin deposited in a bank account with interest rate How much interest was earned in years?
Carleen deposited in a bank account with interest rate How much interest was earned in years?
Hilaria borrowed from her grandfather to pay for college. Five years later, she paid him back the plus interest. What was the rate of interest?
Kenneth lent his niece to buy a computer. Two years later, she paid him back the plus interest. What was the rate of interest?
Lebron lent his daughter to help her buy a condominium. When she sold the condominium four years later, she paid him the plus interest. What was the rate of interest?
Pablo borrowed to start a business. Three years later, he repaid the plus interest. What was the rate of interest?
In years, a bank account that paid earned interest. What was the principal of the account?
In years, a bond that paid earned interest. What was the principal of the bond?
Joshua's computer loan statement said he would pay in interest for a year loan at How much did Joshua borrow to buy the computer?
Margaret's car loan statement said she would pay in interest for a year loan at How much did Margaret borrow to buy the car?
Caitlin invested in an certificate of deposit paying interest. How much interest did she earn form this investment?
Diego invested in a certificate of deposit paying interest. How much interest did he earn form this investment?
Airin borrowed from her parents for the down payment on a car and promised to pay them back in months at a rate of interest. How much interest did she owe her parents?
Yuta borrowed from his brother to pay for his textbooks and promised to pay him back in months at a rate of interest. How much interest did Yuta owe his brother?
Everyday Math
Interest on savings Find the interest rate your local bank pays on savings accounts.
- ⓐ What is the interest rate?
- ⓑ Calculate the amount of interest you would earn on a principal of for years.
Interest on a loan Find the interest rate your local bank charges for a car loan.
- ⓐ What is the interest rate?
- ⓑ Calculate the amount of interest you would pay on a loan of for years.
Writing Exercises
Why do banks pay interest on money deposited in savings accounts?
Why do banks charge interest for lending money?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?