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

Answer:

It is less expensive to keep your old car.

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.

$\text{Number of miles traveled in 5 years}=260\times 250$

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

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

$\text{Gallons of gas used by old car}=\frac{65,000}{24}$

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

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

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

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

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

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

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

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

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

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.

$\text{Gallons of gas used by new car}=\frac{65,000}{53}$

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

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

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

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

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

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

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

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.

Answer 2

It is less expensive to keep your old car