Rebecca is currently working, but is planning to start a college in few years. For this purpose, she would need $20,000. Today she can start investing $750 monthly in an investment account that pays 6 percent compounded monthly. How long would it take her to have enough money to start college?
A)28.5 months
B)27.8 months
C)25.0 months
D)22.6 months
E)30.3 months

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to find out when Rebecca will have enough money to start college:
FV = PMT[((1 + r)^n - 1)/r]
where PMT = $750, r = 0.06/12 = 0.005, and FV = $20,000
20,000 = 750[((1 + 0.005)^n - 1)/0.005]
Solving for n, we get:
n = log(1 + (20000*0.005/750))/log(1.005)
n ≈ 25.0 months
Therefore, it would take Rebecca approximately 25 months to save $20,000 for college. The answer is C.

Rebecca Is Currently Working, but Is Planning to Start a College