Question

Your younger sister, Linda, will start college in five years. She has just informed your parents that she wants to go to Hampton University, which will cost $38,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda’s ambitions, your parents started investing $5,800 per year five years ago and will continue to do so for five more years. Use 12 percent as the appropriate interest rate throughout this problem (for discounting or compounding).

How much will your parents have to save each year (A?) for the next five years in addition to the $5,800 they are currently saving to have the necessary funds for Linda's education? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Additional Annual Saving Required = ________

Answer 1

Let the additional amount saved be x for the next 5 years

The cash flows for the 14 years are

Year	Cash Flow
1	5800
2	5800
3	5800
4	5800
5	5800
6	5800+x
7	5800+x
8	5800+x
9	5800+x
10	5800+x
11	-38000
12	-38000
13	-38000
14	-38000

Since all the savings are used for tuition fees, the sum of present value of all cash flows at time = 0 should be zero

PV = CFn*PV Factor , where PV Factor = 1/(1+r)ⁿ

Given, r = 12%

Year	Cash Flow	PV Factor	PV
1	5800	0.8929	5178.82
2	5800	0.7972	4623.76
3	5800	0.7118	4128.44
4	5800	0.6355	3685.9
5	5800	0.5674	3290.92
6	5800+x	0.5066	0.5066(5800+x)
7	5800+x	0.4523	0.4523(5800+x)
8	5800+x	0.4039	0.4039(5800+x)
9	5800+x	0.3606	0.3606(5800+x)
10	5800+x	0.3220	0.322(5800+x)
11	-38000	0.2875	-10925
12	-38000	0.2567	-9754.6
13	-38000	0.2292	-8709.6
14	-38000	0.2046	-7774.8

Hence, NPV = sum of PV = -16256.16 + 2.0454(5800+x)

=>  -16256.16 + 2.0454(5800+x) = 0

=> 5800 + x = 7947.6679

=> x = 2147.67

Hence, an additional amount of $2147.67 should be saved for the next 5 months