Question

Case 1

The Johnsons Consider Retirement Planning

Harry Johnson’s father, William, was recently forced into early retirement at age 63 because of poor health. In addition to the psychological drawbacks of the unan- ticipated retirement, William’s financial situation is poor because he had not planned adequately for retirement. His situation has inspired Harry and Belinda to take a look at their own retirement planning. Together they now make about $100,000 per year and would like to have a similar level of living when they retire. Harry and Belinda are both 27 years old and recently received their annual Social Security Benefits Statements indicating that they could expect about $28,000 per year in today’s dollars as retirement benefits at age 67. Although their retirement is a long way off, they know that the sooner they put a plan in place, the larger their retirement nest egg will be.

(a) Belinda believes that the couple could maintain their current level of living if their retirement income represented 75 percent of their current annual income after adjusting for inflation. Assuming a 4 percent inflation rate, what would Harry and Belinda’s annual income need to be over and above their Social Security benefits when they retire at age 67?

(b) Both Harry and Belinda are covered by defined- contribution retirement plans at work. Harry’s employer will contribute $1170 per year, and Belinda’s employer will contribute $1140 per year in addition to the $4620 total that Harry and Belinda can contribute. Assuming a 7 percent rate of return, what would their retirement nest egg total 40 years from now?

(c) For how many years would the retirement nest egg provide the amount of income indicated in Question (a)? Assume a 4 percent return after taxes and inflation.

Answer 1

a)	Annual requirement after retirement				=	$100,000*0.75
					=	$75,000
	Amount Available from social security				=	$28,000
	(in present $ terms)
	Additional amount before inflation				=	$75000-$28000
					=	$47,000
	Amount after inflation over security benefits				=	$47000*(1.04)^40
					=	$47000*4.8010
					=	225647.9695
b)	Total amount				=	$1170+$1140+$4620
					=	$6,930
	future value at retirement				=	$6930*FVAF(7%,40 years)
					=	$6930*199.64
					=	$1,383,471.33
c)	To find out these we create the following table
			amount withdrwan
year	opening bal	interest@4%		Closing bal
1	$1,383,471.33	$55,338.85	225647	$1,213,163.18
2	$1,213,163.18	$48,526.53	225647	$1,036,042.71
3	$1,036,042.71	$41,441.71	225647	$851,837.41
4	$851,837.41	$34,073.50	225647	$660,263.91
5	$660,263.91	$26,410.56	225647	$461,027.47
6	$461,027.47	$18,441.10	225647	$253,821.57
7	$253,821.57	$10,152.86	225647	$38,327.43
8	$38,327.43	$1,533.10	225647	($185,786.47)
	since amount becomes -ve in year 8,they can withdraw only upto 7 years
	The saving has been exhausted in just 7 years because they aimed to withdraw $225647 but invested very little amount ($6930) comparetively