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 $22,000 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 10 years at an estimated cost of $387,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $700,000 to his nephew Frodo. He can afford to save $2,300 per month for the next 10 years. 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 11 through 30? rev: 09_17_2012 $2,162.26 $2,206.38 $3,056.76 $2,721.17 $2,250.51

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P
2
3		EAR before retirement	11%
4		EAR after retirement	10%
5		Years to retirement	30	Years
6		Number of Years after retirement	25	Years
7		Monthly withdrawal after the retirement	$22,000
8		Years to purchase cabin	10	Years
9		Cost of cabin	$387,000
10		Amount of inheritance left	$700,000
11		Monthly amount deposited for first ten Years	$2,300
12		Number of years of $2,300 deposits	10	years
13		Let monthly rate be r then EAR can be calculated as follows:
14		EAR = (1+r)12-1
15		Given the EAR, monthly rate r can be calculated as follows:
16		r= (1+EAR)^(1/12)-1
17
18		Effective monthly rate for EAR of 11%	0.87%	=(1+11%)^(1/12)-1
19
20		Effective monthly rate for EAR of 10%	0.80%	=(1+10%)^(1/12)-1
21
22		The monthly deposit from 11-30 years should be such that the present value of requirement equals the present value of deposit.
23
24		Present Value of Requirement	=$387,000*(P/F,0.87%,10*12)+$22,000*(P/A,0.80%,25*12)*(P/F,0.87%,30*12)+$700,000*(P/F,0.80%,25*12)*(P/F,0.87%,30*12)
25			$248,511.66	=D9*(1/((1+D18)^(D8*12)))+D7*PV(D20,D6*12,-1,0)*(1/((1+D18)^(D5*12)))+D10*(1/((1+D20)^(D6*12)))*(1/((1+D18)^(D5*12)))
26
27		Let X be the monthly amount deposited from year 11 to 30 then,
28		Present value of deposit	=$2300*(P/A, 0.87%,10*12)+X*(P/A,0.87%,20*12)*(P/F,0.87%,10*12)
29
30		(P/A, 0.87%,10*12)	74.17	=PV(D18,D12*12,-1,0)
31		(P/A, 0.87%,20*12)	100.29	=PV(D18,(D5-D12)*12,-1,0)
32		(P/F,0.87%,10*12)	0.35	=1/((1+D18)^(D12*12))
33
34		Present value of deposit	=$2300*(P/A, 0.87%,10*12)+X*(P/A,0.87%,20*12)*(P/F,0.87%,10*12)
35			=$2300*74.17+X*100.29*0.35
36			=170583.3+35.3195*X
37
38		Since the present value of requirement and the deposit should be equal therefore
39		$248,511.66 = $170,583.3 + 35.3195*X
40
41		Solving the above equation
42		X	$2,206.38	=(D25-D11*D30)/(D31*D32)
43
44		Hence monthly deposit from year 11 to 30 is	$2,206.38
45		Hence the second option is correct.
46