Bilbo Baggins wants to save money to meet three objectives. First, he would like

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 a EAR of 10 percent before he retires and a EAR of 7 percent EAR after he retires, how much will he have to save each month in years 11 through 30?

Explanation / Answer

PV of after retiremnt requirements at year 30

= 32500 *[1-(1+0.07/12)^- 240]/0.07/12 + 825000/1.07^20

= 4405127.138

amount accumulated after 10 years

= 3800 * [(1+0.1/12)^120 -1]/0.1/12 = 778410.9198

out of this he buys cabin for 405000

amount remaining = 778410 .9198 - 405000 = 373410.92

so th PV of the paymnts from 11 to 30 should be equal to 4031716.218 (4405127.138 - 373410.92)

let x be th monthly saving

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

x = 38906.93

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