Question

On the day of his daughter's birth, a father decided to establish a fund for her college education. The father wants to be able to withdraw $4000 from the fund on her 18th, 19th, 20th and 21st birthdays. If the fund earns interest at 9% per year, compounded quarterly, how much should the father deposit at the end of each year, up through the 17th year?

a.) $465.31 b.) $380.71 c.) $338.41 d.) $423.01 e.) None of the above

Answer 1

Step 1: Calculation of Present Value at the end of 17^thyear:

Amount to be withdrawn each year from 18^th year to 21^st year = 4000

Quarterly Interest rate = 9%/4 = 2.25%

Total quarters in 4 years = 4*4 = 16

Present value of amount withdrawn on 18^th, 19th,, 20th and 21^st at the end of 17^th year = 4000*Present value annuity factor(2.25%,16)

= 4000*13.3126 = 53250.4

Step 2: Calculation of Future Value at the end of 17^th year:

Let the amount to be deposited each year be X.

Total quarters in 17 years = 17*4 = 68

Future value = A/I [(1 + i) ^n – 1]

= X/2.25 %[( 1 + 0.0225) ^68 – 1]

= X/2.25 %[( 1.0225) ^68 – 1]

= X/2.25%*3.540519

= X*(3.540519/2.25%)

= 157.3564X     

Step 3: Calculation of amount to be deposited each year:

Step 1= Step 2

53250.4 = 157.3564X   

X = 53250.4/157.3564

X = $338.4063 i.e. $338.41

Amount to be deposited each year through the 17^th year = $338.41

Answer is c.) $338.41