In: Finance
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?
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