Question

Tiffany and Levi plan to send their son to university. To pay for this they will...

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?

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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

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