Question

Richard and Sue wants to provide full funding for their 3 year old daughter who is expected to start college when she is 18. The current annual cost of a 4 year college is $38,000 which is expected to increase by 3.5% per year. They expect to earn 5% on their investment. They have already saved $13,000 in a college fund for this purpose. Calculate the additional amount they should save by the end of every year in order to accumulate funding for 4 years of college when their daughter turns 18.

$10,298
		$13,809
		$12,638
		$10,133

Answer 1

Calculate annual costs when daughter's education begins
Present value (PV)	$38,000
No of payments (NPER)	15	(18-3)
Expected % increase in costs	3.50%
Future value of per year education costs	Present value*(1+r)^n
Interest rate is r and number of payment is n
Future value of per year education costs	38000*(1.035^15)
Future value of per year education costs	38000*1.675349
Future value of per year education costs	$63,663.26
Calculate total amount that would be required in year 18 in present value term
Real rate of return	(1+nominal rate)/(1+inflation rate) - 1
Real rate of return	(1.05/1.035)-1
Real rate of return	1.45%
Amount required per year	$63,663.26
No of years amount required	4
Interest rate	1.45%
Present value at beginning of 18th year	Annual costs + Annual costs*(1-(1+r^-n)/r)
Present value at beginning of 18th year	63663.26 + 63663.26*(1-(1.0145^-3)/0.0145)
Present value at beginning of 18th year	63663.26 + 63662.26*2.915058
Present value at beginning of 18th year	$249,245
Calculate the additional funding per year required for 4 years using the PMT function
Future value (FV)	$249,245
Present value (PV)	13000
Interest rate (Rate)	5%
No of payment (NPER)	15
Additional funding per year	$10,298	PMT(5%,15,13000,-249245)
Thus, additional funding required per year is $10,298