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 $33,000 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 $410,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $800,000 to his nephew Frodo. He can afford to save $3,900 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.)

    

Monthly savings ?

Answer 1

	EAR before retirement=10%	0.10
	Monthly Rate =i
	(1+i) ^12=1+0.1=1.1
	1+i=(1.1^(1/12))=	1.0079741
	i=0.007974	0.7974%
	EAR after retirement=7%	0.07
	Monthly Rate=r
	r=(1.07^(1/12))-1=	0.005654
	r=0.005654	0.5654%
	Monthly retirement income	$33,000
	Number of months of income	240	(20*12)
	Interest rate during retirement	0.005654
	Inheritence at the end of 20 years	$800,000
	Present value of above cash flows at the time of retirement (30 years from now)	$4,534,918	(Using PV function of excel with Rate=0.005654, Nper=240,Pmt=-33000, FV=-800000)
	Saving during Year 1 through 10 per month	$3,900
	Monthly interest earned on savings	0.7974%
	Number of months(10*12)	120
	Future value of savings at the end of year10	$779,469	(Using FV function of excel with Rate=0.7974%, Nper=120,Pmt=-3900)
	Purchase a cabin in Rivendell	$410,000
	Net Amount available at the end of 10years	$369,469	(779469-369469)
	Future value of this saving at retirement with effective annual interest rate of 10%	$        2,485,603	369469*(1.1^20)
	Required Future value of savings from year 11through 30	$2,049,315	(4534918-2485603)
	Future Value of $1 savings per month for 240 months	$718.26	(Using FV function of excel with Rate=0.7974%, Nper=240,Pmt=-1)
	Amount of monthly savings required from year11 to 30	$          2,853.17	(2049315/718.26)
	Amount of monthly saving from year11 through 30	$          2,853.17