Question

Tiffany and Levi plan to send their son to university. To pay for this they will contribute 9 equal yearly payments to an account bearing interest at the APR of 3.1%, compounded annually. Five years after their last contribution, they will begin the first of five, yearly, withdrawals of $56,400 to pay the university's bills. How large must their yearly contributions be?

Please show your work.

Answer 1

ANSWER:

I = 3.1%

We will find the present value of the withdrawals with the first withdrawal in year 14. (5 years after the last contribution)

pv = withdrawal in year 14(p/f,i,n) + withdrawal in year 15(p/f,i,n) + withdrawal in year 16(p/f,i,n) + withdrawal in year 17(p/f,i,n) + withdrawal in year 18(p/f,i,n)

pv = 56,400(p/f,3.1%,14) + 56,400(p/f,3.1%,15) + 56,400(p/f,3.1%,16) + 56,400(p/f,3.1%,17) + 56,400(p/f,3.1%,18)

pv = 56,400 * 0.6522 + 56,400 * 0.6326 + 56,400 * 0.6136 + 56,400 * 0.5951 + 56,400 * 0.5772

pv = 36,783.90 + 35,677.89 + 34,605.13 + 33,564.62 + 32,555.41

pv = 173,186.95

now we will find the equivalent contribution made in the 1st 9 years.

aw = pv(a/p,i,n)

aw = 173,186.195(a/p,3.1%,9)

aw = 173,186.95 * 0.129

aw = 22,346.92

so the annual equivalent payment is $22,346.92