Question

Mr. S. P. Johnson is creating a college fund for his daughter. He plans to make 7-yearly payments of $10,000 each with the first payment deposited today on his daughter’s 6^th birthday (happy birthday!) Assuming his daughter will need three equal withdrawals from this account to pay for her law-school education beginning when she is twenty-two (i.e. 22, 23, 24), how much will she have on a yearly basis for her law school career? Mr. Johnson expects to earn a constant 10% annual return for the time interval of this problem.

Answer 1

First we calculate the future value at the end of 7 years of the $10000 payments

Using a financial calculator

Set the mode to BGN mode => 2nd BGN => 2nd SET => 2nd QUIT

PV = 0

PMT = 10000

N = 7

I/Y = 10

cpt FV, we get FV = 104358.88

Now, we calculate the equivalent amount at her 22nd birthday (ie. 15 years after 7 years)

Equivalent amount at her 22nd birthday = 104358.88*(1.1^15) =$435932.94

Calculating the yearly basis amount

Using a financial calculator

Set the mode to BGN mode => 2nd BGN => 2nd SET => 2nd QUIT

PV = -435932.94

FV= 0

N = 3

I/Y = 10

cpt PMT, we get PMT= 38149.32

Hence, she will have $38149.32 on a yearly basis for her law school career