Question

Brianna and Ricky plan to send their daughter to university. To pay for this they will contribute 12 equal yearly payments to an account bearing interest at the APR of 9.6%, compounded annually. Four years after their last contribution, they will begin the first of five, yearly, withdrawals of $40,000 to pay the university's bills. How large must their yearly contributions be?

Answer 1

Answer is $5,085.48

Solution:

We can solve this problem with 3 steps, i.e.

Step 1: Find out the present value of annuity of $40,000 for 5 years.

Step 2: Find present value of "answer to Step 1" for 4 years.

Step 3: Use future value of annuity formula, Where future value of annuity will be "answer to Step 2".

Step 1:

|(1+i)" -1 PVA= A i(1+i)n

Where,
PVA = Present Value of Annuity
A = Annuity
i = rate of interest
n = number of years

[(1 + 0.096)5 - 1 PV A = 40000 (0.096(1 + 0.096)

PVA = 153,193.74

Step 2:

PV = FV (1+i)n

FV = Future Value ( 4 years from last payment)
PV = Present Value (Balance amount that should be at the end of last payment)
i = rate of interest
n = number of periods

PV = 153, 193.74 (1 + 0.0964

PV = 106,169.27

Step 3:

(1 + i)" - 1 FVA = A

Where,
FVA = Future Value of Annuity. ($106,269.27 from step 2)
A = Annuity (to find)
i = rate of interest
n = number of years

106,169.27 = A (1 + 0.096) 12-1 0.096

A = 5,085.48

Therefore, their yearly contributions must be $5,085.48.