Question

Consider following situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
You currently drive 325 miles per week in a car that gets 14 miles per gallon of gas. You are considering buying a new fuel-efficient car for S16,000 (after trade-in on your current car that gets 47 miles per gallon
premiums for the new and old car are $1000 and$600 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 pen
ive-year period, is it less expensive to keep your old car or buy the new car?
a five-year period, the cost of the old car iss) and the cost of the new car issThus, over a five-year period, it is less expensive to
and to the nearest dollar as needed

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it is less expensive to purchase a new car

Step-by-step explanation:

The expected cost of gas, insurance, and repairs for the old car are …

Total miles in 5 years = (325 mi/wk)(52 wk/yr)(5 yr) = 84,500 mi

Old car

Gas cost in 5 years = (84,500 mi)/(14 mi/gal)($3.50/gal) =$21,125

Insurance cost in 5 years = (5 yr)($600/yr) =$3,000

Repair cost in 5 years = ($1500/yr)(5 yr) =$7,500

Total operating cost in 5 years = $21125 +3000 +7500 =$31,625

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New Car

Gas cost in 5 years = (84,500 mi)/(47 mi/gal)($3.50/gal) ≈$6,293

Insurance cost in 5 years = (5 yr)($1000/yr) =$5,000

Repair cost in 5 years = (0)(5 yr) = 0

Total operating cost in 5 years = $6293 +5000 = 11,293 __ Difference in operating costs is$31,625 -11,293 = $20,332. It is less expensive to purchase a new car for any price less than$20,300. If the new car costs only \$16,000, it is the less-expensive option.

Purchase of a new car is the least-expensive option.

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