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Prealgebra

6.4 Solve Simple Interest Applications

Prealgebra6.4 Solve Simple Interest Applications
Table of contents
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:
  • Use the simple interest formula
  • Solve simple interest applications

Be Prepared 6.4

Before you get started, take this readiness quiz.

  1. Solve 0.6y=45.0.6y=45.
     If you missed this problem, review Example 5.43.
  2. Solve n1.45=4.6.n1.45=4.6.
     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, P,P, and the bank pays you interest, I.I. The interest is computed as a certain percent of the principal; called the rate of interest, r.r. 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, t,t, represents the number of years the money is left in the account.

Simple Interest

If an amount of money, P,P, the principal, is invested for a period of tt years at an annual interest rate r,r, the amount of interest, I,I, earned is

I=PrtI=Prt

where

I=interestP=principalr=ratet=timeI=interestP=principalr=ratet=time

Interest earned according to this formula is called simple interest.

The formula we use to calculate simple interest is I=Prt.I=Prt. 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 33 years on $500$500 at an interest rate of 6%.6%.

Try It 6.65

Find the simple interest earned after 44 years on $800$800 at an interest rate of 5%.5%.

Try It 6.66

Find the simple interest earned after 22 years on $700$700 at an interest rate of 4%.4%.

In the next example, we will use the simple interest formula to find the principal.

Example 6.34

Find the principal invested if $178$178 interest was earned in 22 years at an interest rate of 4%.4%.

Try It 6.67

Find the principal invested if $495$495 interest was earned in 33 years at an interest rate of 6%.6%.

Try It 6.68

Find the principal invested if $1,246$1,246 interest was earned in 55 years at an interest rate of 7%.7%.

Now we will solve for the rate of interest.

Example 6.35

Find the rate if a principal of $8,200$8,200 earned $3,772$3,772 interest in 44 years.

Try It 6.69

Find the rate if a principal of $5,000$5,000 earned $1,350$1,350 interest in 66 years.

Try It 6.70

Find the rate if a principal of $9,000$9,000 earned $1,755$1,755 interest in 33 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 $12,500$12,500 in her bank account where it will earn 4%4% interest. How much interest will Nathaly earn in 55 years?

Try It 6.71

Areli invested a principal of $950$950 in her bank account with interest rate 3%.3%. How much interest did she earn in 55 years?

Try It 6.72

Susana invested a principal of $36,000$36,000 in her bank account with interest rate 6.5%.6.5%. How much interest did she earn in 33 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 $3,000$3,000 to help him buy a car. In 4 years4 years his brother paid him back the $3,000$3,000 plus $660$660 in interest. What was the rate of interest?

Try It 6.73

Jim lent his sister $5,000$5,000 to help her buy a house. In 33 years, she paid him the $5,000,$5,000, plus $900$900 interest. What was the rate of interest?

Try It 6.74

Hang borrowed $7,500$7,500 from her parents to pay her tuition. In 55 years, she paid them $1,500$1,500 interest in addition to the $7,500$7,500 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 7.5%,7.5%, he would pay $6,596.25$6,596.25 in interest over 55 years. How much did he borrow to pay for his car?

Try It 6.75

Sean's new car loan statement said he would pay $4,866.25$4,866.25 in interest from an interest rate of 8.5%8.5% over 55 years. How much did he borrow to buy his new car?

Try It 6.76

In 55 years, Gloria's bank account earned $2,400$2,400 interest at 5%.5%. 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 $900$900 as graduation gifts and invested it in a 10-month10-month certificate of deposit that earned 2.1%2.1% interest. How much interest did this investment earn?

Try It 6.77

Adriana invested $4,500$4,500 for 88 months in an account that paid 1.9%1.9% interest. How much interest did she earn?

Try It 6.78

Milton invested $2,460$2,460 for 2020 months in an account that paid 3.5%3.5% 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.

202.
Interest Principal Rate Time (years)
$1200$1200 3%3% 55
Table 6.5
203.
Interest Principal Rate Time (years)
$1500$1500 2%2% 44
Table 6.6
204.
Interest Principal Rate Time (years)
$4410$4410 4.5%4.5% 77
Table 6.7
205.
Interest Principal Rate Time (years)
$2212$2212 3.2%3.2% 66
Table 6.8
206.
Interest Principal Rate Time (years)
$577.08$577.08 $4580$4580 22
Table 6.9
207.
Interest Principal Rate Time (years)
$528.12$528.12 $3260$3260 33
Table 6.10

In the following exercises, solve the problem using the simple interest formula.

208.

Find the simple interest earned after 55 years on $600$600 at an interest rate of 3%.3%.

209.

Find the simple interest earned after 44 years on $900$900 at an interest rate of 6%.6%.

210.

Find the simple interest earned after 22 years on $8,950$8,950 at an interest rate of 3.24%.3.24%.

211.

Find the simple interest earned after 33 years on $6,510$6,510 at an interest rate of 2.85%.2.85%.

212.

Find the simple interest earned after 88 years on $15,500$15,500 at an interest rate of 11.425%.11.425%.

213.

Find the simple interest earned after 66 years on $23,900$23,900 at an interest rate of 12.175%.12.175%.

214.

Find the principal invested if $656$656 interest was earned in 55 years at an interest rate of 4%.4%.

215.

Find the principal invested if $177$177 interest was earned in 22 years at an interest rate of 3%.3%.

216.

Find the principal invested if $70.95$70.95 interest was earned in 33 years at an interest rate of 2.75%.2.75%.

217.

Find the principal invested if $636.84$636.84 interest was earned in 66 years at an interest rate of 4.35%.4.35%.

218.

Find the principal invested if $15,222.57$15,222.57 interest was earned in 66 years at an interest rate of 10.28%.10.28%.

219.

Find the principal invested if $10,953.70$10,953.70 interest was earned in 55 years at an interest rate of 11.04%.11.04%.

220.

Find the rate if a principal of $5,400$5,400 earned $432$432 interest in 22 years.

221.

Find the rate if a principal of $2,600$2,600 earned $468$468 interest in 66 years.

222.

Find the rate if a principal of $11,000$11,000 earned $1,815$1,815 interest in 33 years.

223.

Find the rate if a principal of $8,500$8,500 earned $3,230$3,230 interest in 44 years.

Solve Simple Interest Applications

In the following exercises, solve the problem using the simple interest formula.

224.

Casey deposited $1,450$1,450 in a bank account with interest rate 4%.4%. How much interest was earned in 22 years?

225.

Terrence deposited $5,720$5,720 in a bank account with interest rate 6%.6%. How much interest was earned in 44 years?

226.

Robin deposited $31,000$31,000 in a bank account with interest rate 5.2%.5.2%. How much interest was earned in 33 years?

227.

Carleen deposited $16,400$16,400 in a bank account with interest rate 3.9%.3.9%. How much interest was earned in 88 years?

228.

Hilaria borrowed $8,000$8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000,$8,000, plus $1,200$1,200 interest. What was the rate of interest?

229.

Kenneth lent his niece $1,200$1,200 to buy a computer. Two years later, she paid him back the $1,200,$1,200, plus $96$96 interest. What was the rate of interest?

230.

Lebron lent his daughter $20,000$20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000,$20,000, plus $3,000$3,000 interest. What was the rate of interest?

231.

Pablo borrowed $50,000$50,000 to start a business. Three years later, he repaid the $50,000,$50,000, plus $9,375$9,375 interest. What was the rate of interest?

232.

In 1010 years, a bank account that paid 5.25%5.25% earned $18,375$18,375 interest. What was the principal of the account?

233.

In 2525 years, a bond that paid 4.75%4.75% earned $2,375$2,375 interest. What was the principal of the bond?

234.

Joshua's computer loan statement said he would pay $1,244.34$1,244.34 in interest for a 33 year loan at 12.4%.12.4%. How much did Joshua borrow to buy the computer?

235.

Margaret's car loan statement said she would pay $7,683.20$7,683.20 in interest for a 55 year loan at 9.8%.9.8%. How much did Margaret borrow to buy the car?

236.

Caitlin invested $8,200$8,200 in an 18-month18-month certificate of deposit paying 2.7%2.7% interest. How much interest did she earn form this investment?

237.

Diego invested $6,100$6,100 in a 9-month9-month certificate of deposit paying 1.8%1.8% interest. How much interest did he earn form this investment?

238.

Airin borrowed $3,900$3,900 from her parents for the down payment on a car and promised to pay them back in 1515 months at a 4%4% rate of interest. How much interest did she owe her parents?

239.

Yuta borrowed $840$840 from his brother to pay for his textbooks and promised to pay him back in 55 months at a 6%6% rate of interest. How much interest did Yuta owe his brother?

Everyday Math

240.

Interest on savings Find the interest rate your local bank pays on savings accounts.

  1. ⓐ What is the interest rate?
  2. ⓑ Calculate the amount of interest you would earn on a principal of $8,000$8,000 for 55 years.
241.

Interest on a loan Find the interest rate your local bank charges for a car loan.

  1. ⓐ What is the interest rate?
  2. ⓑ Calculate the amount of interest you would pay on a loan of $8,000$8,000 for 55 years.

Writing Exercises

242.

Why do banks pay interest on money deposited in savings accounts?

243.

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?

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