Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2622541 • Letter: B
Question
Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $32,500 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $425,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,325,000 to his nephew Frodo. He can afford to save $4,200 per month for the next 10 years. If he can earn a 10 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 11 through 30?
Explanation / Answer
EAR after Bilbo's retirement = 7%
Effective montly reurn = 1.07^(1/12) -1 = .565%
NPV of
1) Montly returement payment = pv(.565%, 300, 32500,0,0) = 4,688931.73 (at the end of 30 years)
NPV = 4,688,931.73/(1.1^30) = 268,715.8942
2) NPV of inheritence = 1,325,000/[(1.1^30)*(1.07^25) [note he can earn 10% for first 30 years and 7% after that]
= 13,990.74
3) NPV of cabin = 425000/1.1^10 = 163,855.90
Hence NPV of his investments = 446,562.538
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NPV of investment = NPV(4200 for 10 years ) and NPV (xx for next 20 years)
Effective monthly return = 1.1^(1/12) -1 = 0.797%
NPV(4200 for 10 years) = pv(.797%,120, 4200,0,0) = 323,635.91
NPV (xx for next 20 years) = 446,562.538 - 323,635.91 = 122,926.63
=>> PV(.797%,240,xx,0,0)/(1.1^10) = 122,926.63
PV(.797%,240,xx,0,0) = 318,840.02
Hence xx = PMT(.797%,240,318840,0,0) = 2986.38 (ans)
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