CHAPTER 8 Personal Finance

8.6 Cars

Objectives 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.

Mathematics of Financing a Car A 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 is that 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.

Loan Payment Formula for Fixed Installment Loans The 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

Example: Comparing Car Loans Suppose 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.

Example: continued a. Determine the monthly payment and total interest for Loan A.

Example: continued b. Determine the monthly payment and total interest for Loan B.

Example: continued c. Compare $20,000 loan Monthly Payment Total Interest 3-year loan at 7% $618 $2248 5-year loan at 9% $415 $4900

The Leasing Alternative 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. 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 of your estimate.

The Leasing Alternative 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 of the 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 its residual 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 than or equal to the residual value, you owe nothing and you may receive a refund.

Advantages 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 • 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 considerable charges. • 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 than financing 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.

Auto Insurance When you purchase insurance, you buy protection against loss associated with unexpected events. Different types of coverage are associated with auto insurance, but the 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.

Auto Insurance 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.

Example: Saving Money with a Used Car 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 $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-year loan at 8.45%. What is the difference in monthly payments between financing the new car and financing the used car?

Example: (cont) Determine the monthly payments for the new car that costs $25,000, financed with a four-year loan at 7.9%. The monthly payments for the new car are approximately $609.

Example: (cont) Determine the monthly payments for the used car that costs $14,000, financed with a four-year loan at 8.45%. The monthly payments for the used car are approximately $345. The difference in monthly payments between the new-car loan, $609, and the used-car loan, $345, is $609 − $345, or $264.

The Money Pit of Car Ownership 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 on loans.

The Cost of Gasoline

Example: Comparing Fuel Expenses Suppose 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 per gallon? 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 end of six years?

Example: Comparing Fuel Expenses Suppose that you drive 24,000 miles per year and gas averages $4 per gallon. Solution By owning the hybrid rather than the SUV, you save $8000 − $1920, or $6080 in annual fuel expenses

Example: Comparing Fuel Expenses b. Because you save $6080 per year, you save $6080/12 = $507 per month. 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 your future.