SOLUTION: You currently drive 360 miles per week in a car that gets 20 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your curren

Algebra ->  Finance -> SOLUTION: You currently drive 360 miles per week in a car that gets 20 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your curren      Log On


   

Question 1036031: You currently drive 360 miles per week in a car that gets 20 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your current car) that gets 60 miles per gallon. Insurance premiums for the new and old car are $900 and $600 per year, respectively. You anticipate spending $1400 per year on repairs for the old car and no repairs for the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or to buy the new car? By how much?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
360 miles per week * 52 = 18720 miles per year.
18,720 miles per year * 5 = 93600 miles in 5 years.

600 dollars per year insurance * 5 = 3000 dollars in 5 years for the old car.
900 dollars per year insurance * 5 = 4500 dollars in 5 years for the new car.

93600 miles / 20 = 4680 gallons of gas in 5 years for the old car.
93600 miles / 60 = 1560 gallons of gas in 5 years for the new car.

4680 gallons of gas at 3.50 dollars per gallon equals 16380 dollars in 5 years for the old car..
1560 gallons of gas at 3.50 dollars per gallon equals 5460 dollars in 5 years for the new car.

1400 dollars a year car repairs * 5 = 7000 dollars in 5 years for the old car.

the total cost for the new car is 21960 as detailed below.

12000 for the price of the car
4500 for insurance
5460 for gas

the total cost for the old car is 26380 as detailed below.

3000 for insurance
16380 for gas
7000 for repairs

the difference is 26380 - 21960 = 4420.

the new car is less expensive over the 5 years by 4420 dollars.

you can show this in a table as shown below: 



                 old car         new car             old car minus new car

car              0               12000                      -12000
insurance        3000            4500                       -1500
gas              16380           5460                        10920
repairs          7000            0                           7000

total            26380           21960                       4420


the old car is more expensive than the new car by 4420 dollars over the 5 year period.