Question

Consider the following​ situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your​ decision?

You currently drive 275 miles per week in a car that gets 21 miles per gallon of gas. You are considering buying a new​ fuel-efficient car for ​$20,000 ​(after trade-in on your current​ car) that gets 47 miles per gallon. Insurance premiums for the new and old car are ​$800 and ​$600 per​ year, respectively. You anticipate spending ​$1000 per year on repairs for the old car and having no repairs on the new car. Assume gas costs ​$4.00 per gallon. Over a​ five-year period, is it less expensive to keep your old car or buy the new​ car?



Over a​ five-year period, the cost of the old car is ​$enter your response here and the cost of the new car is ​$enter your response here. ​Thus, over a​ five-year period, it is less expensive to
▼
keep your old car.
buy the new car.

Answer 1

Old car

Explanation:

To determine the cost of the old car over a five-year period, we need to calculate the cost of gas, insurance, and repairs for five years.

Gas cost per week = (275 miles / 21 miles per gallon) x $4.00 per gallon = $53.81

Gas cost per year = $53.81 x 52 weeks = $2,798.12

Gas cost for five years = $2,798.12 x 5 = $13,990.60

Insurance cost for five years = $600 x 5 = $3,000

Repairs cost for five years = $1,000 x 5 = $5,000

Total cost for old car over five years = $13,990.60 + $3,000 + $5,000 = $21,990.60

To determine the cost of the new car over a five-year period, we need to calculate the cost of the car plus the cost of gas and insurance for five years.

Cost of new car = $20,000

Gas cost per week = (275 miles / 47 miles per gallon) x $4.00 per gallon = $19.15

Gas cost per year = $19.15 x 52 weeks = $996.80

Gas cost for five years = $996.80 x 5 = $4,984.00

Insurance cost for five years = $800 x 5 = $4,000

Total cost for new car over five years = $20,000 + $4,984.00 + $4,000 = $28,984.00

Therefore, over a five-year period, it is less expensive to keep your old car, as it costs $21,990.60 compared to the cost of $28,984.00 for the new car.

However, there might be other factors to consider, such as the value of your time spent on repairs, the potential resale value of the new car, and any environmental factors related to the fuel efficiency of the new car.