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.
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 ...
SUV purchase decision based on present value calculations.