Question

In: Finance

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?

Solutions

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


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