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 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 will be better to keep the old car.
`\left[\begin{array}{cccc}$&$New&$Old&$Differential\\$purchase&-14000&&14000\\$Gasoline spending&-4292&-9479&-5187\\$repairs&&-7500&-7500\\$insurance&-4000&-2000&2000\\$Result&-22292&-18979&3313\\\end{array}\right]`

Step-by-step explanation:

gasoline spending:

old:

250 miles per week/ 24 miles per gallon= 10,41666666

then that x 52 weeks per year x 3.5 per gallon x 5 years

new:

250 / 53 = 4,716981

then this x 52 weeks x 3.5 per gallon x 5 years=

repairs:

1,500 x 5 years = 7,500

insurance:

800 x 5 = 4,000 new car insurance

400 x 5 = 2,000 old car insurance