Question

1. Nancy just had a new baby boy and plans to send him to college 19 years from now. She wants to deposit each winter in an education account which pays 10% (compounded annually) so that her boy will have enough money set aside that he can take out $20,000 at the beginning of each year to pay tuition, room and board, etc., for each of his four-year education. How much will Nancy need to deposit at the end of each year in order to meet the goal (Note: There will be 19 total deposits and the first deposit will be made in one year. Also, the last deposit will be made the day before the first withdrawal.)

Hint: 0-19: ordinary annuity, you deposit PMT every year for 19 times;

19-23: annuity due, you withdraw 20,000 every year for 4 times.

Can you get the PVA of those four 20,000 @ point 19? The number you get is the future value of those 19 pmts. Then use that value as FV of the ordinary annuity (the 19 pmts), can you get the PMT?

a. 1,363.14

b. 1,379.89

c. 1,306.64

d. 1,312.84

e. 1,321.12

Answer 1

Step 1 -Calculation of accumulated amount in a education fund at the end of 19 years
We can use the present value of annuity due formula to calculate this amount.
Present Value of annuity due = P + P{[1 - (1+r)^-(n-1)]/r}
Present value of annuity due = accumulated amount in a education fund at the end of 19 years = ?
P = withdrwal amount from the education fund at the beginning of the each year = $20,000
r = interest rate per year = 10%
n = number of withdrawals = 4
Present Value of annuity due = 20000 + 20000{[1 - (1+0.10)^-(4-1)]/0.10}
Present Value of annuity due = 20000 + 20000 x 2.486852
Present Value of annuity due = 69737.04
Accumulated amount in a education fund at the end of 19 years = $69,737.04
Step 2 - Calculation of yearly deposits in a education furn for 19 years
We can use the future value of annuity formula to calculate the yearly deposit to a education fund.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = Accumulated amount in a education fund at the end of 19 years = $69,737.04
P = Yearly deposit to a education fund = ?
r = interest rate per year = 10%
n = number of yearly deposits = 19
69737.04 = P x {[(1+0.10)^19 -1]/0.10}
69737.04 = P x 51.15909
P = 1363.14
Nancy need to deposit $1,363.14 at the end of each year in order to meet the goal.
The answer is Option a.