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) 21.25 months
B) 27.78 months
C) 25.10 months
D) 22.56 months
E) 30.25 months

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity:
FV = PMT x (((1 + r)^n - 1) / r)
Where,
PMT = $750
r = 6%/12 = 0.005 (monthly interest rate)
FV = $20,000

Now we can solve for n:
n = (ln(1 + (FV x r / PMT))) / (ln(1 + r))
n = (ln(1 + (20000 x 0.005 / 750))) / (ln(1 + 0.005))
n = 25.10

Therefore, it will take Rebecca 25.10 months to have enough money to start college.

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