You estimate that it will take five years to complete your college education. Your parents want to invest enough money today at an interest rate of 8% compounded annually to allow you to withdraw $10,000 at the end of each year for the next five years, with nothing left at the end. The amount of money to invest today is:
A) $14,690.
B) $34,050.
C) $39,930.
D) $50,000.
E) None of the other answers are correct.

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity due:

PV = PMT[(1 - (1 + r/n)^(-nt))/(r/n)] * (1 + r/n)

where PV is the present value, PMT is the payment per period (in this case, $10,000 for 5 years), r is the annual interest rate (0.08), n is the number of times the interest is compounded per year (1), and t is the number of years in the annuity (5).

Plugging in the values, we get:

PV = $10,000[(1 - (1 + 0.08/1)^(-1*5))/(0.08/1)] * (1 + 0.08/1)
PV = $39,930.16

Therefore, the amount of money to invest today is $39,930.16. The correct answer choice is C.

You Estimate That It Will Take Five Years to Complete