Question

Jane is a newborn. Her parents are planning to contribute $4,000 a year (or possibly less) towards her college fund into an account that will grow at a constant rate of 4.5% a year. Both parents work for the same company that offered to match parental contributions dollar for dollar for the first 5 parental deposits and 30 cents for every parental dollar for subsequent parental deposits, until Jane reaches 19. Once she reaches 19, both the company and parents stop their contributions. College costs are expected to be $40,000 a year and Jane spends 4 years in college once she reaches 19. Assume that the beginning balance on the account is $25,000 What is the smallest amount parents should contribute each year to make Jane's college affordable?

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M
2
3		Interest rate	4.50%
4		Education cost per year	$40,000
5		Number of years at college	4
6		Initial deposit	$25,000
7		The present value amount required at the 19th year should be equal to FV of the amount deposited for 19 years.
8
9		Present value of amount required at 19th birthdays	=$40000*(P/A,4.5%,4)
10			$143,501.03
11
12		Assuming the annual deposit made by parents is A, then
13
14		Future value of Deposits at Year 19	=25000*(F/P,4.5%,19)+2A*(F/A,4.5%,5)*(F/P,4.5%,14)+1.3A*(F/A,4.5%,14)
15
16		(F/P,4.5%,19)	2.31	=(1+D3)^19
17		(F/A,4.5%,5)	5.47	=FV(D3,5,-1,0)
18		(F/P,4.5%,14)	1.85	=(1+D3)^14
19		(F/A,4.5%,14)	18.93	=FV(D3,14,-1,0)
20
21		Future value of Deposits at Year 19	=25000*(F/P,4.5%,19)+2A*(F/A,4.5%,5)*(F/P,4.5%,14)+1.3A*(F/A,4.5%,14)
22			=25000*2.31+2A*5.47*1.85+1.3A*18.93
23			=57696.51+44.87A
24
25		Since the present value of the required amount at year 19should be equal to the future value of amount deposited at year 19 therefore
26		$143,501.03 =$57,696.51+44.87A
27
28		Solving the above equation,
29		A	$1,912.09	=(D10-D16*D6)/(2*D17*D18+1.3*D19)
30
31		Hence annual deposit required is	$1,912.09
32