8.6 CARS. Objective 1 Compute the monthly payment and interest costs for a car loan.
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1 8.6 CARS Objective 1 Compute the monthly payment and inteest costs fo a ca loan. Suppose that you decide to boow $15,000 fo a new ca. You can select one of the following loans, each equiing egula monthly payments: Installment Loan A: fou-yea loan at 8% Installment Loan B: six-yea loan at 10%. a. Find the monthly payments and the total inteest fo Loan A. b. Find the monthly payments and the total inteest fo Loan B. c. Compae the monthly payments and total inteest fo the two loans. a. P ( n ) 0.08 ( 12 ) ,000 PMT = =» - nt -12(4) n 12 $366 Total inteest fo loan A: $ $15,000 = $2568 b. P ( n ) 0.10 ( 12 ) ,000 PMT = =» $278 - nt -12(6) n 12
2 Total inteest fo loan B: $ $15,000 = $5016 c. Monthly payments ae lowe with the longe-tem loan, but thee is moe inteest with the longe-tem loan. Objective 2 Undestand the types of leasing contacts. Leasing is the pactice of paying a specified amount of money ove a specified time fo the use of a poduct. Thee ae two types of leasing contacts: 1. A closed-end lease: Each month, you make a fixed payment based on estimated usage. 2. An open-end lease: Each month you make a fixed payment based on the ca s esidual value. Residual value is the estimated esale value of the ca at the end of the lease and is detemined by the deale. Objective 3 Undestand the pos and cons of leasing vesus buying a ca. Leasing a ca offes both advantages and disadvantages ove buying one. Lists of pos and cons of leasing can be found on page 548.
3 Objective 4 Undestand the diffeent kinds of ca insuance. When you puchase insuance, you buy potection against loss associated with unexpected events. Diffeent types of coveage ae associated with auto insuance, but the one equied by nealy evey state is liability. Thee ae two components of liability coveage: Bodily injuy liability coves the costs of lawsuits if someone is injued o killed in an accident in which you ae at fault. Popety damage liability coves damage to othe cas and popety fom negligent opeation of you vehicle. If you have a ca loan o lease a ca, you will also need collision and compehensive coveage: Collision coveage pays fo damage o loss of you ca if you e in an accident. Compehensive coveage potects you ca fom peils such as fie, theft, falling objects, acts of natue, and collision with an animal.
4 Objective 5 Compae monthly payments on new and used cas. Used cas ae a good option fo many people. You best buy is typically a two- to thee-yea-old ca because the annual depeciation in pice is geatest ove the fist few yeas. The two most commonly used souces of picing infomation fo used cas ae the National Automobile Deales Association Official Used Ca Guide ( and the Kelley Blue Book Used Ca Guide ( EXAMPLE Suppose that you ae thinking about buying a ca and have naowed down you choices to two options: The new-ca option: The new cas costs $19,000 and can be financed with a thee-yea loan at 6.18%. The used-ca option: A two-yea-old model of the same ca costs $11,500 and can be financed with a thee-yea loan at 7.5% What is the diffeence in monthly payments between financing the new ca and financing the used ca? New ca: P ( n ) ( 12 ) ,000 PMT = =» $580 - nt -12(3) n 12
5 Used ca: P ( n ) ( 12 ) ,500 PMT = =» - nt -12(3) n 12 $358 The diffeence is $580 - $358 = $222 Objective 6 Solve poblems elated to owning and opeating a ca. A lage potion of a ca s opeating expenses involves the cost of gasoline. The Cost of Gasoline: annual miles diven Annual fuel expense = miles pe gallon pice pe gallon EXAMPLE Suppose that you dive 36,000 miles pe yea and gas aveages $3.50 pe gallon. a. What will you save in annual fuel expenses by owning a hybid ca aveaging 40 miles pe gallon athe than an SUV aveaging 15 miles pe gallon? b. If you deposit you monthly fuel savings at the end of the month into an annuity that pays 7.25% compounded monthly, how much will you have saved at the end of the seven yeas? Round all computations to the neaest dolla.
6 a. Annual fuel expense fo the hybid annual miles diven = pice pe gallon miles pe gallon b. 36,000 = $ = $3150 Annual fuel expense fo the SUV annual miles diven = pice pe gallon miles pe gallon 36,000 = $ = $8400 The diffeence is $ $3150 = $5250
7 8.6 PRACTICE 1) Suppose that you decide to boow $15,000 fo a new ca. You can select one of the following loans, each equiing egula monthly payments: Installment Loan A: thee-yea loan at 5.1% Installment Loan B: five-yea loan at 6.4%. a. Find the monthly payments and the total inteest fo Loan A. b. Find the monthly payments and the total inteest fo Loan B. c. Compae the monthly payments and the total inteest fo the two loans. 2) Suppose that you ae thinking about buying a ca and have naowed down you choices to two options: The new-ca option: The new ca costs $28,000 and can be financed with a fou-yea loan at 6.12%. The used-ca option: A thee-yea old model of the same ca costs $16,000 and can be financed with a fou-yea loan at 6.86%. What is the diffeence in monthly payments between financing the new ca and financing the used ca?
8 3) Suppose that you dive 40,000 miles pe yea and gas aveages $4 pe gallon. a. What will you save in annual fuel expenses by owning a hybid ca aveaging 40 miles pe gallon athe than an SUV aveaging 16 miles pe gallon? b. If you deposit you monthly fuel savings at the end of each month into an annuity that pays 5.2% compounded monthly, how much will you have saved at the end of six yeas?
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