Tom wishes to buy another boat in five years that presently costs $150,000. He expects the...

Tom wishes to buy another boat in five years that presently costs $150,000. He expects the cost of the boat to increase due to inflation by 3% per year for the next two years and 5% per year the following three years. He also wants to spend $75,000 per year for 6 years beginning at the end of 12 years from today. How much must he save each year for the next 5 years if he can earn 6% on his investments?

Expert Solution

Cost of Boat after 5 years = 150000+3%+3%+5%+5%+5% = $184218.65

Year	Discounting Factor [1/(1.06^year)]	Cash Flow	PV of Cash Flows (cash flow*discounting factor)
1	0.943396226		0
2	0.88999644		0
3	0.839619283		0
4	0.792093663		0
5	0.747258173	184218.65	137658.8918
6	0.70496054		0
7	0.665057114		0
8	0.627412371		0
9	0.591898464		0
10	0.558394777		0
11	0.526787525		0
12	0.496969364	75000	37272.70227
13	0.468839022	75000	35162.92667
14	0.442300964	75000	33172.57233
15	0.417265061	75000	31294.87956
16	0.393646284	75000	29523.47128
17	0.371364419	75000	27852.33139
		Present Value of All Spendings, as on today = Sum of PVs	331937.7753

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 331937.7753, i = Interest Rate = 0.06, n = Number of Periods = 5

Therefore,

331937.7753 = P*[1-{(1+0.06)^-5}]/0.06

19916.266518 = P*0.2527418

Therefore, Amount to be saved = Annuity = P = 19916.266518/0.2527418 = $78800.83

jeff jeffy answered 2 years ago

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