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:
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
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