Question

Suppose that you are 22 today and that your salary for the year ending today is $61,250. Suppose that you are paid on an annual basis at the end of each year; so you are receiving $61,250 today. You plan to retire at age 68and will need 75% of your last year’s salary for your annual living expenses starting at age 69. You have saved $50,000 to date. All living expenses between now and retirement will be covered by your annual salary in each year. All living expenses after retirement will be covered by your retirement income. Assume that your first withdrawal from your retirement account for post-retirement income occurs on your 69thbirthdayand that you next deposit into your retirement account will be one year from now. You have some older relatives that have always had an interest in you and have indicated that you are in their wills. Assume that you will inherit $100,000 when you turn 36. Assume also that, given the state of health care costs and a family history of healthcare issues, that you will need to have an amount of $1.25 million available by age 57 to cover healthcare costs above and beyond what your health insurance plan is likely to cover. Assume that you will save 10% of your annual income while you work, and that you will not save any additional amount after you retire. You project that your salary will grow at a rate of 5% and that your retirement income needs will grow at 3%to reflect long-term inflation forecasts. The higher growth rate in your salary reflects your expectation that you will receive promotions and that absent promotions your salary will keep pace with inflation. The appropriate interest rate for your working life is 9% and declines to 6% after you retire. How much will you have to leave to your heirs if you live to age 90?

Answer 1

		Number of years to retire	46	(68-22)
		Salary before retirement (Last Salary)	$             577,848	(61250*(1.05^46)
		First withdrawal age 69	$             433,386	(0.75*577848)
		Salary at end of year 1	$               64,313	(1.05*61250)
		Salary at end of year (N+1)=1.05*(Salary at end of year (N)
		Present Value(PV) of cash flow=(Cash flow)/((1+i)^N)
		i=Interest rate, N=Year of cash flow
		ANNUAL CASH FLOW IN SAVINGS ACCOUNT BEFORE RETIREMENT:
		Interest Rate=9%=0.09
		N	A	B=0.1*A	C	D	E=B+C+D	F=E/(1.09^N)
	Age	Year	Salary	Savings	Inheritance	Healthcare cost	Net Savings	PV of Savings
	23	1	$               64,313	$            6,431			$              6,431	$            5,900
	24	2	$               67,528	$            6,753			$              6,753	$            5,684
	25	3	$               70,905	$            7,090			$              7,090	$            5,475
	26	4	$               74,450	$            7,445			$              7,445	$            5,274
	27	5	$               78,172	$            7,817			$              7,817	$            5,081
	28	6	$               82,081	$            8,208			$              8,208	$            4,894
	29	7	$               86,185	$            8,618			$              8,618	$            4,715
	30	8	$               90,494	$            9,049			$              9,049	$            4,542
	31	9	$               95,019	$            9,502			$              9,502	$            4,375
	32	10	$               99,770	$            9,977			$              9,977	$            4,214
	33	11	$             104,758	$         10,476			$            10,476	$            4,060
	34	12	$             109,996	$         11,000			$            11,000	$            3,911
	35	13	$             115,496	$         11,550			$            11,550	$            3,767
	36	14	$             121,271	$         12,127	$100,000		$          112,127	$          33,554
	37	15	$             127,334	$         12,733			$            12,733	$            3,496
	38	16	$             133,701	$         13,370			$            13,370	$            3,368
	39	17	$             140,386	$         14,039			$            14,039	$            3,244
	40	18	$             147,405	$         14,741			$            14,741	$            3,125
	41	19	$             154,776	$         15,478			$            15,478	$            3,010
	42	20	$             162,514	$         16,251			$            16,251	$            2,900
	43	21	$             170,640	$         17,064			$            17,064	$            2,793
	44	22	$             179,172	$         17,917			$            17,917	$            2,691
	45	23	$             188,131	$         18,813			$            18,813	$            2,592
	46	24	$             197,537	$         19,754			$            19,754	$            2,497
	47	25	$             207,414	$         20,741			$            20,741	$            2,405
	48	26	$             217,785	$         21,778			$            21,778	$            2,317
	49	27	$             228,674	$         22,867			$            22,867	$            2,232
	50	28	$             240,108	$         24,011			$            24,011	$            2,150
	51	29	$             252,113	$         25,211			$            25,211	$            2,071
	52	30	$             264,719	$         26,472			$            26,472	$            1,995
	53	31	$             277,955	$         27,795			$            27,795	$            1,922
	54	32	$             291,853	$         29,185			$            29,185	$            1,851
	55	33	$             306,445	$         30,645			$            30,645	$            1,784
	56	34	$             321,768	$         32,177			$            32,177	$            1,718
	57	35	$             337,856	$         33,786		($1,250,000)	$    (1,216,214)	$       (59,578)
	58	36	$             354,749	$         35,475			$            35,475	$            1,594
	59	37	$             372,486	$         37,249			$            37,249	$            1,536
	60	38	$             391,110	$         39,111			$            39,111	$            1,479
	61	39	$             410,666	$         41,067			$            41,067	$            1,425
	62	40	$             431,199	$         43,120			$            43,120	$            1,373
	63	41	$             452,759	$         45,276			$            45,276	$            1,322
	64	42	$             475,397	$         47,540			$            47,540	$            1,274
	65	43	$             499,167	$         49,917			$            49,917	$            1,227
	66	44	$             524,125	$         52,413			$            52,413	$            1,182
	67	45	$             550,332	$         55,033			$            55,033	$            1,139
	68	46	$             577,848	$         57,785			$            57,785	$            1,097
							SUM	$       100,678
		Present Value of net savings till retirement	$             100,678
		Future Value of net savings at Retirement	$         5,303,380	(100678*(1.09^46)
		CASH FLOWS AFTER RETIREMENT
		Inflation rate=3%
		Withdrawal in year 2(Age70)=1.03*433386=	$       446,387.82
		Withdrawal in year (N+1)=1.03*(Withdrawal in year (N+1)
		Interest rate=6%=0.06
		N	A	B=A/(1.06^N)
	Age	YEAR	Withdrawal	PV of Withdrawal
	69	1	$             433,386	$       408,855
	70	2	$             446,388	$       397,284
	71	3	$             459,779	$       386,040
	72	4	$             473,573	$       375,114
	73	5	$             487,780	$       364,498
	74	6	$             502,413	$       354,182
	75	7	$             517,486	$       344,158
	76	8	$             533,010	$       334,417
	77	9	$             549,001	$       324,953
	78	10	$             565,471	$       315,756
	79	11	$             582,435	$       306,819
	80	12	$             599,908	$       298,136
	81	13	$             617,905	$       289,698
	82	14	$             636,442	$       281,499
	83	15	$             655,536	$       273,532
	84	16	$             675,202	$       265,791
	85	17	$             695,458	$       258,268
	86	18	$             716,321	$       250,959
	87	19	$             737,811	$       243,856
	88	20	$             759,945	$       236,955
	89	21	$             782,744	$       230,248
	90	22	$             806,226	$       223,732
			SUM	$   6,764,748
		Present value at Retirement needed for living expenses	$         6,764,748
		Amount available at retirement	$         5,303,380
		Shortfall	$         1,461,368
		PV of Amount of inheritance	$       (1,461,368)
		Amount left at age 90	$       (5,266,093)	(-1461368*(1.06^22)