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 and explain steps.

Answer 1

Step 1: Calculate the present value of the five yearly withdrawals of $56400

R = 3.1%

PW of the withdrawals = (56400*(1-1/1.031^5)/.031)*(1/1.031^14)

PW of the withdrawals = 167979.6

Step 2: Calculate the present value of the 9 yearly annual deposits

Let, annual deposit = P

PW of annual deposits = P*(1-1/1.031^9)/.031

Step 3: Equating both the PW to find out P

P*(1-1/1.031^9)/.031 = 167979.6

P = 167979.6 / ((1-1/1.031^9)/.031)

P = $21675

So, 9 yearly equal payments will be $21675.