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8/2/2017 Thinking Mathematically, Sixth Edition

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8 Personal Finance > 8.6 Cars

8.6 Cars

What am I Supposed to Learn?After you have read this section, you should be able to:

1 Compute the monthly payment and interest costs for a car loan.

2 Understand the types of leasing contracts.

3 Understand the pros and cons of leasing versus buying a car.

4 Understand the different kinds of car insurance.

5 Compare monthly payments on new and used cars.

6 Solve problems related to owning and operating a car.

TO THE GUYS AT RYDELL HIGH IN THE musical Grease!, Kenickie's new car looks like a hunk of junk, but to him it's Greased Lightnin', a hot-rodding work of art onwheels. As with many teens, Kenickie's first car is a rite of passage—a symbol of emerging adulthood.

Our love affair with cars began in the early 1900s when Henry Ford cranked out the first Model T. Since then, we've admired cars to the point of identifying with thevehicles we drive. Cars can serve as status symbols, providing unique insights into a driver's personality.

In this section, we view cars from another vantage point—money. The money pit of owning a car ranges from financing the purchase to escalating costs of everythingfrom fuel to tires to insurance. We open the section with the main reason people spend more money on a car than they can afford: financing.

The Mathematics of Financing a CarA loan that you pay off with weekly or monthly payments, or payments in some other time period, is called an installment loan. The advantage of an installment loan isthat the consumer gets to use a product immediately. The disadvantage is that the interest can add a substantial amount to the cost of a purchase.

Let's begin with car loans in which you make regular monthly payments, called fixed installment loans. Suppose that you borrow P dollars at interest rate r over tyears.

To find your regular payment amount, PMT, we set the amount the lender expects to receive equal to the amount you will save in the annuity:

Solving this equation for PMT, we obtain a formula for the loan payment for any installment loan, including payments on car loans.

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The lender expects

A dollars at the end of t years.▼

A = P (1 + )r

n

nt

You save the A dollars in an annuity by paying

PMT dollars n times per year.▼

A =PMT[ −1](1+ )r

n

nt

( )r

n

P = .(1 + )r

n

ntP MT [ − 1](1 + )r

n

nt

( )r

n

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8 Personal Finance > 8.6 Cars

1 Compute the monthly payment and interest costs for a car loan.

Loan Payment Formula for Fixed Installment LoansThe regular payment amount, PMT, required to repay a loan of P dollars paid n times per year over t years at an annual rate r is given by

TechnologyHere are the calculator keystrokes to compute

Begin by simplifying the exponent, to avoid possible errors with parentheses:

Scientific and graphing calculator keystrokes require placing parentheses around the expressions in both the numerator and the denominator.

Many Scientific Calculators

Many Graphing Calculators

Answers may vary if you do calculations in stages and round along the way.

Example 1 Comparing Car LoansSuppose that you decide to borrow $20,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:

Installment Loan A: three-year loan at 7%

Installment Loan B: five-year loan at 9%.

a. Find the monthly payments and the total interest for Loan A.

b. Find the monthly payments and the total interest for Loan B.

c. Compare the monthly payments and total interest for the two loans.

SOLUTION

For each loan, we use the loan payment formula to compute the monthly payments.

a. We first determine monthly payments and total interest for Loan A.

d

The monthly payments are approximately $618.



P MT = .P ( )r

n

[1 − ](1 + )rn

−nt

.20,000 ( )0.07

12

[1 − ](1 + )0.07

12

−12(3)

−12 (3) , to − 36

.20,000 ( )0.07

12

[1 − ](1 + )0.07

12

−36

20000 .07 12 1 1 .07 12 36( × ÷ ) ÷ ( − ( + ÷ ) yx +/− ) =

20000 .07 12 1 1 .07 12 36( × ÷ ) ÷ ( − ( + ÷ ) ∧ (−) ) ENTER







Page 540

Now we calculate the interest over three years, or 36 months.

The total interest paid over three years is approximately $2248.

b. Next, we determine monthly payments and total interest for Loan B.

d

The monthly payments are approximately $415.


Total interest

over 3 years

=Total of all

monthly paymentsminus

amount of

the loan.

▼ ▼ ▼ ▼ ▼

= $618 × 36 − $20,000

= $2248








Page 541

8 Personal Finance > 8.6 Cars > The Leasing Alternative

Now we calculate the interest over five years, or 60 months.

The total interest paid over five years is approximately $4900.

c. Table 8.6 compares the monthly payments and total interest for the two loans.

TABLE 8.6 Comparing Car Loans$20,000 loan Monthly Payment Total Interest3-year loan at 7% $618 $22485-year loan at 9% $415 $4900

Check Point 1Suppose that you decide to borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:

Installment Loan A: four-year loan at 8%

Installment Loan B: six-year loan at 10%.



c. Compare the monthly payments and total interest for the two loans.

Blitzer BonusFinancing Your Car

• Check out financing options. It's a good idea to get preapproved for a car loan through a bank or credit union before going to the dealer. You can then compare theloan offered by the dealer to your preapproved loan. Furthermore, with more money in hand, you'll have more negotiating power.

• Dealer financing often costs 1% or 2% more than a bank or credit union. Shop around for interest rates. Credit unions traditionally offer the best rates on car loans,more than 1.5% less on average than a bank loan.

• Put down as much money as you can. Interest rates generally decrease as the money you put down toward the car increases. Furthermore, you'll be borrowingless money, thereby paying less interest.

• A general rule is that you should spend no more than 20% of your net monthly income on a car payment.

The Leasing Alternative

2 Understand the types of leasing contracts.

Leasing is the practice of paying a specified amount of money over a specified time for the use of a product. Leasing is essentially a long-term rental agreement.

Leasing a car instead of buying one has become increasingly popular over the past several years. There are two types of leasing contracts:

• A closed-end lease: Each month, you make a fixed payment based on estimated usage. When the lease ends, you return the car and pay for mileage in excess ofyour estimate.




Total interest

over 5 years

=Total of all

monthly paymentsminus

amount of

the loan.

▼ ▼ ▼ ▼ ▼

= $415 × 60 − $20,000

= $4900

▲

Monthly payments are less

with the longer-term loan.

▲

Interest is more with the

longer-term loan.













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8 Personal Finance > 8.6 Cars > The Importance of Auto Insurance

• An open-end lease: Each month you make a fixed payment based on the car's residual value. Residual value is the estimated resale value of the car at the end ofthe lease and is determined by the dealer. When the lease ends, you return the car and make a payment based on its appraised value at that time compared to itsresidual value. If the appraised value is less than the residual value stated in the lease, you pay all or a portion of the difference. If the appraised value is greater thanor equal to the residual value, you owe nothing and you may receive a refund.

Leasing a car offers both advantages and disadvantages over buying one.

3 Understand the pros and cons of leasing versus buying a car.

Advantages of Leasing

• Leases require only a small down payment, or no down payment at all.

• Lease payments for a new car are lower than loan payments for the same car. Most people can lease a more expensive car than they would be able to buy.

• When the lease ends, you return the car to the dealer and do not have to be concerned about selling the car.

Disadvantages of Leasing

• When the lease ends, you do not own the car.

• Most lease agreements have mileage limits: 12,000 to 15,000 miles per year is common. If you exceed the number of miles allowed, there can be considerablecharges.

• When mileage penalties and other costs at the end of the leasing period are taken into consideration, the total cost of leasing is almost always more expensive thanfinancing a car.

• While leasing the car, you are responsible for keeping it in perfect condition. You are liable for any damage to the car.

• Leasing does not cover maintenance.

• There are penalties for ending the lease early.

Car leases tend to be extremely complicated. It can appear that there are as many lease deals as there are kinds of cars. A helpful pamphlet entitled “Keys to VehicleLeasing” is published by the Federal Reserve Board. Copies are available on the Internet. Additional information can be found at websites such as home.autos.msn.comor intellichoice.com.

The Importance of Auto Insurance

4 Understand the different kinds of car insurance.

Who needs auto insurance? The simple answer is that if you own or lease a car, you do.

When you purchase insurance, you buy protection against loss associated with unexpected events. Different types of coverage are associated with auto insurance, butthe one required by nearly every state is liability. There are two components of liability coverage:

• Bodily injury liability covers the costs of lawsuits if someone is injured or killed in an accident in which you are at fault.

• Property damage liability covers damage to other cars and property from negligent operation of your vehicle.

If you have a car loan or lease a car, you will also need collision and comprehensive coverage:

• Collision coverage pays for damage or loss of your car if you're in an accident.

• Comprehensive coverage protects your car from perils such as fire, theft, falling objects, acts of nature, and collision with an animal.

There is a big difference in auto insurance rates, so be sure to shop around. Insurance can be very expensive for younger drivers with limited driving experience. A poordriving record dramatically increases your insurance rates. Other factors that impact your insurance premium include where you live, the number of miles you drive eachyear, and the value of your car.







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8 Personal Finance > 8.6 Cars > New or Used?

New or Used?

5 Compare monthly payments on new and used cars.

Who insists you need a new car? A new car loses an average of 12% of its value the moment it is driven off the dealer'slot. It's already a used car and you haven't even arrived home.

Used cars are a good option for many people. Your best buy is typically a two-to three-year-old car because the annualdepreciation in price is greatest over the first few years. Furthermore, many sources of financing for used cars will loanmoney only on newer models that are less than five years old. Reputable car dealerships offer a good selection of usedcars, with extended warranties and other perks.

The two most commonly used sources of pricing information for used cars are the National Automobile DealersAssociation Official Used Car Guide (www.nada.com) and the Kelley Blue Book Used Car Guide (www.kbb.com). Theycontain the average retail price for many different makes of used cars.

Example 2 Saving Money with a Used CarSuppose that you are thinking about buying a car and have narrowed down your choices to two options:

• The new-car option: The new car costs $25,000 and can be financed with a four-year loan at 7.9%.

• The used-car option: A three-year-old model of the same car costs $14,000 and can be financed with a four-yearloan at 8.45%.

What is the difference in monthly payments between financing the new car and financing the used car?

SOLUTION

We first determine the monthly payments for the new car that costs $25,000, financed with a four-year loan at 7.9%.

d

The monthly payments for the new car are approximately $609. Now we determine the monthly payments for the usedcar that costs $14,000, financed with a four-year loan at 8.45%.

d

The monthly payments for the used car are approximately $345. The difference in monthly payments between thenew-car loan, $609, and the used-car loan, $345, is

You save $264 each month over a period of four years with the used-car option.

Table of Contents



$609 − $345, or $264.

Thinking Mathematically, SixthEdition

1 Problem Solving and CriticalThinking

2 Set Theory

2.1 Basic Set Concepts

Methods for Representing Sets

The Empty Set

Notations for Set Membership

Sets of Natural Numbers

Cardinality and Equivalent Sets

Finite and Infinite Sets

Equal Sets

Concept and VocabularyCheck

Exercise Set 2.1

2.2 Subsets

2.3 Venn Diagrams and SetOperations

2.4 Set Operations and VennDiagrams with Three Sets

2.5 Survey Problems

Chapter Summary, Review, andTest

Chapter 2 Test

3 Logic

4 Number Representation andCalculation

5 Number Theory and the RealNumber System

6 Algebra: Equations andInequalities

7 Algebra: Graphs, Functionsand Linear Systems

8 Personal Finance

9 Measurement

10 Geometry

11 Counting Methods andProbability Theory

12 Statistics

13 Voting and Apportionment

14 Graph Theory

Answers to Selected Exercises

Credits

Subject Index




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8 Personal Finance > 8.6 Cars > The Money Pit of Car Ownership

Check Point 2Suppose that you are thinking about buying a car and have narrowed down your choices to two options:

The new-car option: The new car costs $19,000 and can be financed with a three-year loan at 6.18%.

The used-car option: A two-year-old model of the same car costs $11,500 and can be financed with a three-year loan at 7.5%.


The Money Pit of Car Ownership

6 Solve problems related to owning and operating a car.

Buying a car is a huge expense. To make matters worse, the car continues costing money after you purchase it. These costs include operating expenses such as fuel,maintenance, tires, tolls, parking, and cleaning. The costs also include ownership expenses such as insurance, license fees, registration fees, taxes, and interest onloans.

The significant expense of owning and operating a car is shown in Table 8.7. According to the American Automobile Association (AAA), the average yearly cost ofowning and operating a car is just under $9000.

TABLE 8.7 Annual Costs of Owning and Operating a Car in 2012 *Type of Car Small Sedan Medium Sedan Minivan Large Sedan SUV 4WD

Cost per mileCost per year $6735 $8780 $9504 $11,324 $11,360Source: AAA

A large portion of a car's operating expenses involves the cost of gasoline. As the luster of big gas-guzzlers becomes less appealing, many people are turning to fuel-efficient hybrid cars that use a combination of gasoline and rechargeable batteries as power sources.

Our next example compares fuel expenses for a gas-guzzler and a hybrid. You can estimate the annual fuel expense for a vehicle if you know approximately how manymiles the vehicle will be driven each year, how many miles the vehicle can be driven per gallon of gasoline, and how much a gallon of gasoline will cost.

The Cost of Gasoline

Example 3 Comparing Fuel ExpensesSuppose that you drive 24,000 miles per year and gas averages $4 per gallon.

a. What will you save in annual fuel expenses by owning a hybrid car averaging 50 miles per gallon rather than an SUV (sport utility vehicle) averaging 12 miles pergallon?

b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 7.3% compounded monthly, how much will you have saved at the endof six years?

* Based on driving 15,000 miles per year.




44.9¢ 58.5¢ 63.4¢ 75.5¢ 75.7¢

Annual fuel expense = × price per gallonannual miles driven

miles per gallon













Page 545

8 Personal Finance > 8.6 Cars > The Money Pit of Car Ownership

SOLUTION

a. We use the formula for annual fuel expense.

Your annual fuel expense is $1920 for the hybrid and $8000 for the SUV. By owning the hybrid rather than the SUV, you save

in annual fuel expenses.

b. Because you save $6080 per year, you save

or approximately $507 per month. Now you deposit $507 at the end of each month into an annuity that pays 7.3% compounded monthly. We use the formula for thevalue of an annuity to determine your savings at the end of six years.

You will have saved approximately $45,634 at the end of six years. This illustrates how driving a car that consumes less gas can yield significant savings for yourfuture.

Check Point 3Suppose that you drive 36,000 miles per year and gas averages $3.50 per gallon.

a. What will you save in annual fuel expenses by owning a hybrid car averaging 40 miles per gallon rather than an SUV averaging 15 miles per gallon?

b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 7.25% compounded monthly, how much will you have saved at theend of seven years? Round all computations to the nearest dollar.




Annual fuel expense = × price per gallonannual miles drivenmiles per gallon

Annual fuel expense for the hybrid = × $4 = 480 × $4 = $192024,000

50▲

The hybrid averages 50 miles per gallon.

Annual fuel expense for the SUV = × $4 = 2000 × $4 = $800024,000

12▲

The SUV averages 12 miles per gallon.

$8000 − $1920, or $6080

≈ $507,$6080

12

A

A

=P[ −1](1+ )r

n

nt

( )r

n

=507[ −1](1+ )0.073

12

12⋅6

( )0.073

12

≈ 45,634

Use the formula for the value of an annuity.

The annuity involves month-end deposits of

$507 : P = 507. The interest rate is 7.3%:

r = 0.073. The interest is compounded

monthly: n = 12. The number of years is 6: t = 6.

Use a calculator.













8 Personal Finance > 8.6 Cars > Concept and Vocabulary Check

Concept and Vocabulary CheckFill in each blank so that the resulting statement is true.

1. In the formula

___________________ is the regular payment amount required to repay a loan of ___________________ dollars paid ___________________ times per year over___________________ years at an annual interest rate ___________________.

2. The two types of contracts involved with leasing a car are called a/an ___________________ lease and a/an ___________________ lease.

3. The estimated resale value of a car at the end of its lease is called the car's _____________________.

4. There are two components of liability insurance. The component that covers costs if someone is injured or killed in an accident in which you are at fault is called_____________________ liability. The component that covers damage to other cars if you are at fault is called ________________________ liability.

5. The type of car insurance that pays for damage or loss of your car if you're in an accident is called ___________________ coverage.

6. The type of insurance that pays for damage to your car due to fire, theft, or falling objects is called ______________________ coverage.

In Exercises 7–12, determine whether each statement is true or false. If the statement is false, make the necessary changes(s) to produce a true statement.

7. The interest on a car loan can be determined by taking the difference between the total of all monthly payments and the amount of the loan. ______

8. When an open-end lease terminates and the car's appraised value is less than the residual value stated in the lease, you owe nothing. ______

9. One advantage to leasing a car is that you are not responsible for any damage to the car. ______

10. One disadvantage to leasing a car is that most lease agreements have mileage limits. ______

11. Collision coverage pays for damage to another car if you cause an accident. ______

12. Due to operating and ownership expenses, a car continues costing money after you buy it. ______

Exercise Set 8.6Practice and Application ExercisesIn Exercises 1–10, use

Round answers to the nearest dollar.

1. Suppose that you borrow $10,000 for four years at 8% toward the purchase of a car. Find the monthly payments and the total interest for the loan.

2. Suppose that you borrow $30,000 for four years at 8% for the purchase of a car. Find the monthly payments and the total interest for the loan.

3. Suppose that you decide to borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:

Installment Loan A: three-year loan at 5.1%

Installment Loan B: five-year loan at 6.4%.



c. Compare the monthly payments and the total interest for the two loans.

4. Suppose that you decide to borrow $40,000 for a new car. You can select one of the following loans, each requiring regular monthly payments:

Installment Loan A: three-year loan at 6.1%

Installment Loan B: five-year loan at 7.2%.



c. Compare the monthly payments and the total interest for the two loans.

5. Suppose that you are thinking about buying a car and have narrowed down your choices to two options:

The new-car option: The new car costs $28,000 and can be financed with a four-year loan at 6.12%.

The used-car option: A three-year old model of the same car costs $16,000 and can be financed with a four-year loan at 6.86%.



P MT = ,P ( )r

n

[1− ](1+ )r

n

−nt

P MT = .P ( )r

n

[1 − ](1 + )r

n

−nt








Page 546


6. Suppose that you are thinking about buying a car and have narrowed down your choices to two options:

The new-car option: The new car costs $68,000 and can be financed with a four-year loan at 7.14%.

The used-car option: A three-year old model of the same car costs $28,000 and can be financed with a four-year loan at 7.92%.










8 Personal Finance > 8.6 Cars > Concept and Vocabulary Check

7. Suppose that you decide to buy a car for $29,635, including taxes and license fees. You saved $9000 for a down payment and can get a five-year car loan at6.62%. Find the monthly payment and the total interest for the loan.

8. Suppose that you decide to buy a car for $37,925, including taxes and license fees. You saved $12,000 for a down payment and can get a five-year loan at 6.58%.Find the monthly payment and the total interest for the loan.

9. Suppose that you are buying a car for $60,000, including taxes and license fees. You saved $10,000 for a down payment. The dealer is offering you two incentives:

Incentive A is $5000 off the price of the car, followed by a five-year loan at 7.34%.

Incentive B does not have a cash rebate, but provides free financing (no interest) over five years.

What is the difference in monthly payments between the two offers? Which incentive is the better deal?

10. Suppose that you are buying a car for $56,000, including taxes and license fees. You saved $8000 for a down payment. The dealer is offering you two incentives:

Incentive A is $10,000 off the price of the car, followed by a four-year loan at 12.5%.

Incentive B does not have a cash rebate, but provides free financing (no interest) over four years.

What is the difference in monthly payments between the two offers? Which incentive is the better deal?

In Exercises 11–14, use the formula

Round all computations to the nearest dollar.

11. Suppose that you drive 40,000 miles per year and gas averages $4 per gallon.



12. Suppose that you drive 15,000 miles per year and gas averages $3.50 per gallon.



The table shows the expense of operating and owning four selected cars, by average costs per mile. Use the appropriate information in the table to solve Exercises 13–16.

AVERAGE ANNUAL COSTS OF OWNING ANDOPERATING A CAR

Average Costs per MileMake and Model Operating Ownership Total

Cadillac STS $0.26 $0.72 $0.98Mercury Grand Marquis GS $0.23 $0.42 $0.65Honda Accord LX $0.21 $0.34 $0.55Toyota Corolla CE $0.15 $0.25 $0.40

Source: Runzheimer International

13.

a. If you drive 20,000 miles per year, what is the total annual expense for a Cadillac STS?

b. If the total annual expense for a Cadillac STS is deposited at the end of each year into an IRA paying 8.5% compounded yearly, how much will be saved at theend of six years?

14.

a. If you drive 14,000 miles per year, what is the total annual expense for a Toyota Corolla CE?

b. If the total annual expense for a Toyota Corolla CE is deposited at the end of each year into an IRA paying 8.2% compounded yearly, how much will be saved atthe end of six years?

15. If you drive 30,000 miles per year, by how much does the total annual expense for a Cadillac STS exceed that of a Toyota Corolla CE over six years?

16. If you drive 25,000 miles per year, by how much does the total annual expense for a Mercury Grand Marquis GS exceed that of a Honda Accord LX over sixyears?

Writing in Mathematics17. If a three-year car loan has the same interest rate as a six-year car loan, how do the monthly payments and the total interest compare for the two loans?



A = .

P [ − 1](1 + )r

n

nt

( )r

n








Page 547

18. What is the difference between a closed-end car lease and an open-end car lease?

19. Describe two advantages of leasing a car over buying one.

20. Describe two disadvantages of leasing a car over buying one.

21. What are the two components of liability coverage and what is covered by each component?

22. What does collision coverage pay for?

23. What does comprehensive coverage pay for?

24. How can you estimate a car's annual fuel expense?

Critical Thinking ExercisesMake Sense? In Exercises 25–30, determine whether each statement makes sense or does not make sense, and explain your reasoning.

25. If I purchase a car using money that I've saved, I can eliminate paying interest on a car loan, but then I have to give up the interest income I could have earned onmy savings.









8 Personal Finance > 8.7 The Cost of Home Ownership

26. The problem with my car lease is that when it ends, I have to be concerned about selling the car.

27. Although lease payments for a new car are lower than loan payments for the same car, once I take mileage penalties and other costs into consideration, the totalcost of leasing is more expensive than financing the car.

28. I've paid off my car loan, so I am not required to have liability coverage.

29. Buying a used car or a fuel-efficient car can yield significant savings for my future.

30. Because it is extremely expensive to own and operate a car, I plan to look closely at whether or not a car is essential and consider other modes of transportation.

31. Use the discussion at the bottom of page 539 to prove the loan payment formula shown in the box at the top of page 540. Work with the equation in which theamount the lender expects to receive is equal to the amount saved in the annuity. Multiply both sides of this equation by and then solve for PMT by dividing both

sides by the appropriate expression. Finally, divide the numerator and the denominator of the resulting formula for PMT by to obtain the form of the loanpayment formula shown in the box.

32. The unpaid balance of an installment loan is equal to the present value of the remaining payments. The unpaid balance, P, is given by

where PMT is the regular payment amount, r is the annual interest rate, n is the number of payments per year, and t is the number of years remaining in the loan.

a. Use the loan payment formula to derive the unpaid balance formula.

b. The price of a car is $24,000. You have saved 20% of the price as a down payment. After the down payment, the balance is financed with a 5-year loan at 9%.Determine the unpaid balance after three years. Round all calculations to the nearest dollar.

Group Exercises33. Group members should go to the Internet and select a car that they might like to buy. Price the car and its options. Then find two loans with the best rates, but withdifferent terms. For each loan, calculate the monthly payments and total interest.

34. Student Loans

Group members should present a report on federal loans to finance college costs, including Stafford loans, Perkins loans, and PLUS loans. Also include a discussionof grants that do not have to be repaid, such as Pell Grants and National Merit Scholarships. Refer to Funding Education Beyond High School, published by theDepartment of Education and available at studentaid.ed.gov. Use the loan repayment formula that we applied to car loans to determine regular payments and intereston some of the loan options presented in your report.

8.7 The Cost of Home Ownership

What am I Supposed to Learn?After you have read this section, you should be able to:

1 Compute the monthly payment and interest costs for a mortgage.

2 Prepare a partial loan amortization schedule.

3 Solve problems involving what you can afford to spend for a mortgage.

4 Understand the pros and cons of renting versus buying.

THE BIGGEST SINGLE PURCHASE THAT MOST PEOPLE make in their lives is the purchase of a home. If you choose home ownership at some point in the future, itis likely that you will finance the purchase with an installment loan. Knowing the unique issues surrounding the purchase of a home, and whether or not this aspect of theAmerican dream is right for you, can play a significant role in your financial future.



r

n

(1 + )r

n

nt

P = P MT ,[1− ](1+ )r

n

−nt

( )r

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MortgagesA mortgage is a long-term installment loan (perhaps up to 30, 40, or even 50 years) for the purpose of buying a home, and for which the property is pledged as securityfor payment. If payments are not made on the loan, the lender may take possession of the property. The down payment is the portion of the sale price of the home thatthe buyer initially pays to the seller. The minimum required down payment is computed as a percentage of the sale price. For example, suppose you decide to buy a$220,000 home. The lender requires you to pay the seller 10% of the sale price. You must pay 10% of $220,000, which is or $22,000, to the seller.Thus, $22,000 is the down payment. The amount of the mortgage is the difference between the sale price and the down payment. For your $220,000 home, theamount of the mortgage is or $198,000.

Monthly payments for a mortgage depend on the amount of the mortgage (the principal), the interest rate, and the duration of the mortgage. Mortgages can have a fixedinterest rate or a variable interest rate.


0.10 × 220,000

$220,000 − $22,000,






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