Thanks Assume a world without inflation Janice Lewisberg 38

Assume a world without inflation. Janice Lewisberg, 38, plans to retire at age Her life expectancy is age 90. She wants to live a retirement lifestyle that will cost $35,000 per year, payable at the beginning of each year. She now has $20,000 in her investment account and plans to invest an equal amount annu- ally for her retirement. The rate of interest that she expects to earn is 6%. 68.

Solution

Answer )

Current Age = 38 years , retirement age = 68 years, life expectancy = 90 years, Periodic annuity amount (P) = $35,000,

investment terms (t) = 68-38= 30 years

Annuity payment term (n) = 90-68 = 22 years at beginning of each year.

Return rate (r) = 6%

Value of annuity (A) = (P (1- (1 + r)^-n) / r)) * (1 + r) ------- eq(1)

where, P = periodic payment , n = no of periods

Answer a)

Using eq(1) , Retirement corpus = ( 35000*(1- (1+0.06)^-22)/ 0.06)* (1.06) = $ 446742.7

Answer B)

To calculate the annual investment made by investors , ( at the end of year)

FV of annuity = P [ ((1+r)^t -1) /r)

=> periodic payment (P) = FV /  [ ((1+r)^t -1) /r) ]

Here, in the question , the FV = $ 446,742.7 , r = 6% , t= 30 years

P = 446742.7 / (((1+6%)^30) - 1) / 6% = $ 5,650.81 each year

Answer (C)

If he dies at age of 85 , it means will not recieve the annuity payment due at beginning of age 86 .

Balance transfer to her estate = $ 147,432.78

Answer D )

Now all calculation at r= 8%

Using eq(1) , Retirement corpus = ( 35000*(1- (1+0.08)^-22)/ 0.08)* (1.08) = $ 385588.1

Amount to be saved each year ,

periodic payment (P) = FV /  [ ((1+r)^t -1) /r) ]

=>P = 385588.1 / (((1+8%)^30) - 1) / 8% =$ 3403.76

The calculation of balance payment transfer to her Estate.

Remaining balance = $ 139,744.82

calculated below

Age	Annuity value	Annuity Paid	Balance end of year
69	$446,742.70	$35,000	$411,742.70
70	$436,447.26	$35,000	$401,447.26
71	$425,534.10	$35,000	$390,534.10
72	$413,966.14	$35,000	$378,966.14
73	$401,704.11	$35,000	$366,704.11
74	$388,706.36	$35,000	$353,706.36
75	$374,928.74	$35,000	$339,928.74
76	$360,324.46	$35,000	$325,324.46
77	$344,843.93	$35,000	$309,843.93
78	$328,434.57	$35,000	$293,434.57
79	$311,040.64	$35,000	$276,040.64
80	$292,603.08	$35,000	$257,603.08
81	$273,059.27	$35,000	$238,059.27
82	$252,342.82	$35,000	$217,342.82
83	$230,383.39	$35,000	$195,383.39
84	$207,106.40	$35,000	$172,106.40
85	$182,432.78	$35,000	$147,432.78
86	$156,278.75	$35,000	$121,278.75
87	$128,555.47	$35,000	$93,555.47
88	$99,168.80	$35,000	$64,168.80
89	$68,018.93	$35,000	$33,018.93
90	$35,000.06	$35,000	$0.06