You currently drive $240$ miles per week in a car that gets $24$ miles per gallon of gas. You are considering buying a new fuel-efficient car for $\$ 13,000$ (after trade-in on your current car) that gets $40$ miles per gallon. Insurance premiums for the new and old car are $\$ 720$ and $\$ 500$ per year, respectively. You anticipate spending $\$ 1050$ per year on repairs for the old car and having no repairs on the new car. Assume gas costs $\$ 2.45$ per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?

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Q. You currently drive

240

miles per week in a car that gets

24

miles per gallon of gas. You are considering buying a new fuel-efficient car for

\$ 13,000

(after trade-in on your current car) that gets

40

miles per gallon. Insurance premiums for the new and old car are

\$ 720

and

\$ 500

per year, respectively. You anticipate spending

\$ 1050

per year on repairs for the old car and having no repairs on the new car. Assume gas costs

\$ 2.45

per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?

Calculate total miles driven: Calculate the total miles driven in $7$ years. $\newline$ $240$ miles/week $*$ $52$ weeks/year $*$ $7$ years $=$ $87360$ miles
Calculate total gas used (old car): Calculate the total gallons of gas used by the old car. $\newline$ $87360 \, \text{miles} / 24 \, \text{miles/gallon} = 3640 \, \text{gallons}$
Calculate total gas cost (old car): Calculate the total cost of gas for the old car. $3640$ gallons * \$$2. $45$ /gallon = \\(8918$
Calculate total gas used (new car): Calculate the total gallons of gas used by the new car. $87360$ miles / $40$ miles/gallon = $2184$ gallons
Calculate total gas cost (new car): Calculate the total cost of gas for the new car. $2184 \text{ gallons} * \$2.45/\text{gallon} = \$5355.6$
Calculate insurance cost (old car): Calculate the total insurance cost for the old car. $\newline$ $\$500/year \times 7 \text{ years} = \$3500$
Calculate insurance cost (new car): Calculate the total insurance cost for the new car. $\$720/year \times 7 \text{ years} = \$5040$
Calculate repair costs (old car): Calculate the total repair costs for the old car. $\$1050/year \times 7 years = \$7350$
Calculate total cost (old car): Calculate the total cost of the old car over $7$ years. $\$8918$ (gas) + $\$3500$ (insurance) + $\$7350$ (repairs) = $\$19768$
Calculate total cost (new car): Calculate the total cost of the new car over $7$ years. $\$5355.6$ (gas) + $\$5040$ (insurance) + $\$0$ (repairs) + $\$13000$ (purchase) = $\$23395.6$
Calculate cost difference: Calculate the difference in total costs between the old and new car. $\$23395.6$ (new car) - $\$19768$ (old car) = $\$3627.6$
End of calculations: End of calculations. The new car is more expensive over $7$ years by $\$3627.6$ .