Question

You currently drive 250 miles per week in a car that gets 24 miles per gallon of gas. You are considering buying a new​ fuel-efficient car for ​$14 comma 000 ​(after trade-in on your current​ car) that gets 53 miles per gallon. Insurance premiums for the new and old car are ​$800 and ​$400 per​ year, respectively. You anticipate spending ​$1500 per year on repairs for the old car and having no repairs on 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 buy the new​ car?

Answer 1

It is less expensive to keep your old car

Answer 2

It is less expensive to keep your old car.

Step-by-step explanation:

We have been given that you currently drive 250 miles per week in a car that gets 24 miles per gallon of gas.

1 year equals 52 weeks.

5 years equals 260 weeks.

`\text{Number of miles traveled in 5 years}=260* 250`

`\text{Number of miles traveled in 5 years}=65,000`

The old car gives a mileage of 24 miles per gallon of gas.

`\text{Gallons of gas used by old car}=(65,000)/(24)`

`\text{Gallons of gas used by old car}=2708.33`

`\text{Cost of gas used by old car}=2708.33* \$3.50`

`\text{Cost of gas used by old car}=\$9479.155`

`\text{Insurance premium for old car for 5 years}=\$400* 5`

`\text{Insurance premium for old car for 5 years}=\$2,000`

`\text{Amount spent on repairs for old car}=\$1500* 5`

`\text{Amount spent on repairs for old car}=\$7500`

`\text{Total cost of using old car for 5 years}=\$7500+\$9479.155+\$2,000`

`\text{Total cost of using old car for 5 years}=\$18979.155`

Therefore, the total of using old car for 5 years is $18979.16.

We are told that new car gives a mileage of 53 miles per gallon.

`\text{Gallons of gas used by new car}=(65,000)/(53)`

`\text{Gallons of gas used by new car}=1226.415`

`\text{Cost of gas used by new car}=\$3.50* 1226.415`

`\text{Cost of gas used by new car}=\$4292.45`

`\text{Insurance premium for new car for 5 years}=\$800* 5`

`\text{Insurance premium for new car for 5 years}=\$4,000`

`\text{Total cost of using new car for 5 years}=\$14,000+\$4292.45+\$4000`

`\text{Total cost of using new car for 5 years}=\$22292.45`

Since the cost of using new car for 5 years is greater than cost of using old car for 5 years, therefore, it is less expensive to keep your old car.