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 a retirement income of $32,500 per month for 20 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 $405,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $825,000 to his nephew Frodo. He can afford to save $3,800 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Present value of after retiremnt requirements at year 30

= 32500 *[1-(1+0.07/12)^- 240]/0.07/12 + 825000/1.07^20 = $4,405,127.138

Amount accumulated after 10 years = 3800 * [(1+0.1/12)^120 -1]/0.1/12 = $778,410.9198

Out of this he buys cabin for = $405,000

Amount remaining = $778,410 .9198 - $405,000 = $373,410.92

So th PV of the payments from 11 to 30 should be equal to $4,031,716.218 (4405127.138 - 373410.92)

Let x be the monthly saving

x * [1 -(1+0.1/12)^-240]/0.1/12 = 4031716.218

x = $38,906.93