To determine which model is the better decision, we need to calculate the total cost of owning each car for 4 years.
For Model A:
Trade-in value after 4 years: $28,000 * 52% = $14,560
Net cost of Model A after 4 years: $28,000 - $14,560 = $13,440
For Model B:
Trade-in value after 4 years: $18,000 * 26% = $4,680
Net cost of Model B after 4 years: $18,000 - $4,680 = $13,320
Now we need to calculate the present value of these costs to compare them accurately.
Present value of Model A:
PV(A) = $13,440 / (1 + 7%)^4 = $10,294.31
Present value of Model B:
PV(B) = $13,320 / (1 + 7%)^4 = $10,217.27
Comparing the present values, we can see that Model B has a lower cost than Model A. The difference in cost is: $10,294.31 - $10,217.27 = $77.04
Therefore, Model B is the better financial decision and it is $77.04 "cheaper" than Model A.
Jessica is in the market for a new car. She has narrowed her search down to 2 models. Model A costs $28,000 and Model B costs $18,000. With both cars she plans to pay cash and own them for 4 years before trading in for a new car. Her research indicates that the trade in value for Model A after 4 years is 52% of the initial purchase price, while the trade in value for Model B is 26%. Jessica has no emotional attachment to either model and wants to make a strictly financial decision. The interest rate is 7%. 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?
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