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?

Answer 1

Answer:

During retirement period:

He will withdraw retirement income of $32,500 per month at the end of the month for 20 years and 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.

Hence:

Number of monthly withdrawals = 20 * 12 = 240

FV = $825,000

PMT = $32,500

Monthly interest rate = 7%/12

To calculate retirement fund required at time when he retires = PV (rate, nper, pmt, fv, type)

= PV (7%/12, 240, -32500, -825000, 0)

= $4,396,203.15

Hence:

Retirement fund required at time when he retires (30 years from now) = $4,396,203.15

Further:

He can afford to save $3,800 per month for the next 10 years. He can earn an EAR of 10 percent before he retires.

FV after 10 years = FV(rate, nper, pmt, pv, type) = FV(10%/12, 120, -3800, 0,0) = $778410.92

Now given that:

He would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $405,000.

Remaining balance after 10 years = $778410.92 - 405000 = $373,410.92

Value of this remaining balance at the time of retirement = FV (10%/12, 240, 0, -373410.92, 0) = $2,736,382.72

Remaining balance of retirement fund required to be funded = $4,396,203.15 - $2,736,382.72 = $1,659,820.43

Hence:

Amount he will have to save each month in Years 11 through 30 = PMT(10%/12, 240, 0, -1659820.43,0) = $2,185.79

Amount he will have to save each month in Years 11 through 30 = $2,185.79