Gracie Shay wants to buy a new Hummer in five years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now at a rate of 6% compounded semiannually, she:

Question

Quizplus · Accepted Answer

We can use the formula for future value of a lump sum:
FV = PV (1 + r/n)^(nt)
where: 
PV = present value = $12,000
r = annual interest rate = 6% = 0.06
n = number of times compounded per year = 2 (semiannually)
t = number of years = 5

Plugging in the values, we get:
FV = 12,000 (1 + 0.06/2)^(2*5)
FV = 12,000 (1.03)^10
FV = $16,126.80

Therefore, Gracie will have $16,126.80 in five years, which is less than the cost of the Hummer. Therefore, the answer is D, Gracie will not have enough money to buy the Hummer.

Gracie Shay Wants to Buy a New Hummer in Five