Jessica is in the market for a new car. She has narrowed her search down to 2 mo

Question

Jessica is in the market for a new car. She has narrowed her search down to 2 models. Model A costs $24,000 and Model B costs $18,000. With both cars she plans to pay cash and own them for 3 years before trading in for a new car. Her research indicates that the trade in value for Model A after 3 years is 50% of the initial purchase price, while the trade in value for Model B is 25%. Jessica has no emotional attachment to either model and wants to make a strictly financial decision. The interest rate is 6%. For simplicity assume that operating and maintenance costs for the models are identical every year. Which model is the better decision and how much "cheaper" is it than the alternative?

Explanation / Answer

Model A is cheaper. model A is cheaper by $353.904 to model B.

Model A:

Total cost is 24000*(1+.06)^3= 28584.384

after 3 yrs trade in value is 50% of 24000= 12000

total expanses is 28584.384-12000=16584.384

Model B:

total cost is 18000*(1+.06)^3= 21438.288

trade in value is 25% of 18000 ie, 4500

so total expenses is 21438.288-4500= 16938.288

so model A is cheaper by $353.904.

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