Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2702082 • 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 $29,000 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 15 years at an estimated cost of $659,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $800,000 to his nephew Frodo. He can afford to save $1,900 per month for the next 15 years.
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Required: If he can earn a 11 percent EAR before he retires and a 10 percent EAR after he retires, how much will he have to save each month in years 16 through 30?Explanation / Answer
Value of the retirement income and Frodo's inheritance is calculated in Excel is =PV(10%/12,25*12,-29000,-800000). This is equal to 3,257,721 (as of time of retirement).
Value of savings in first 15 years as of year 15 =FV(11%/12,15*12,-1900,0,0). This is equal to 863,910. After deducting $659,000 for the cabin, this leaves 204,910. The future value of this at time of retirement is 204,910 * (1+11%)^15 = 980,411
So difference is 3,257,721 - 980,411 = 2,277,310 which is the future value of the savings from year 16 to 30
Let montly savings be X. So the payment required can be calculated in Excel as =PMT(11%/12,15*12,0,-B6). This is equal to $5,008.
Hope this helped ! Let me know in case of any queries.
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