Question

Anne starts to work for XYZ Company when she is 24 years old, making $66,000 per year. One of the benefits she is offered is voluntary contribution to a 401-K plan Although she would like to maximize her contributions, Anne calculates that she will only be able to afford to contribute 6% of her salary at first. Assuming that she receives salary increases of 3% each year and stabilizes her expenses, she intends to increase the contribution to 8% of her salary when she is 35 years old and to 10% when she is 45 years old. Anne believes that she will be able to live comfortably if she receives $60,000 per year from the 401 K plan in each year of her retirement. The actuarial estimate of her life expectancy is 85 and the assumed discount is 7%. Required: Given the assumptions, how much will Anne have in her 401-K when she is 55? Will Anne be able to retire at 55 years old and receive the benefits she anticipates needing? If Anne lived to age 90, would she have enough in the 401-K to continue receiving payments at this level? What changes in the assumptions could negatively affect Anne's retirement plan?

Answer 1

Please see below answer step wise with all Reference point + complete formula at different age bracket - FV of 401 k Plan.

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As per Question
Anne received $ 60000 per year
from 401 K Plan in each year fo her retirement
Actual estimated life	85
Discount rate	7%
At Age year	55
We need to calculate Discount factor ( present value)
Year Difference ( 85-55)	30
(1.07^30-1)/(0.07*1.07^30) (a)	12.409041
Anne receive ($)(b)	60,000
She needs as per 401 K plan(a*b)$	7,44,542
Age phase wise contribution
She receives salary 3% each year
Age gap between ( 25 year to 34 Year)
Salary Increase	3%	Ref Number
Discount rate( '7% *3%)	1.102
Initial Contribution ( $ 66000*6%)$ (C)	3,960
We have contributed ( 35 year-25 year)	11
FV at the age of 35 under 401 K(C*D)$	74,180	A
(1.102^11-1)/(1.102-1) (D)	19
Initial Contribution ( $ 66000*6%)$	3,960
We have contributed ( 44 year-35 year)	10
Discount rate( '7% *3%)	1.102
Initial Contribution ( $ 66000*8%*1.03^10)$	7,096	B
FV at the age of 45 under 401 K( C+D) $	2,60,106	E
(A*1.07^10)+((B*1.102^10-1)/(1.102-1))
(A*1.07^10)	1,45,923	C
((B*1.102^10-1)/(1.102-1))	1,14,182	D
We have contributed ( 54 year-45 year)	10
Discount rate( '7% *3%)	1.102
Initial Contribution ( $ 66000*10%*1.03^20)$	11,920	F
FV at the age of 55 under 401 K $(G+H)	7,03,473	I
(E*1.07^10)	5,11,668	G
((F*1.102^10-1)/(1.102-1))	1,91,806	H
Ultimately we reached conclusion that
at the age of 55 years she will receives$	7,03,473
Where as she needs ($)	7,44,542
So she can not take retirement at age of 55

Also eventhough she lived 90 years still not able to fulfill her requirement

Negative impact - If discount rate goes below 7% and salary increment goes below 3%