# Present value purchase decision

A married couple is planning to buy a new sport utility vehicle (SUV) 5 years from now. They expect the SUV to cost $32,000 at the time of purchase. (a) If they want to have half of the cost for a down payment, how much must they save each year (starting at the end of the current year) if they can earn 10% per year on their saving. Alternatively, (b) they can set aside a lump sum 2 years from now in a savings account that earns 10% annual (compound) interest in order to have their down payment. How much should this lump sum of money be? (c) If they choose to deposit 5 equal end-of-year amounts in the savings account in order to pay in full for the SUV 5 years from now, what will be the equivalent annual worth? (d) What is the equivalent present value of the SUV? Assume the same interest rate.

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#### Solution Preview

To find the amount we need to save each year, we need to use the future value of an annuity formula:

FV = A (1+i)^n -1 / i

This gives us:

16000= A ((1.1)^5 ...

#### Solution Summary

SUV purchase decision based on present value calculations.