Question

Ann is now 25 years old and she is planning to start saving for retirement. She expects her income of $60,000 in the coming year to grow at the (nominal) rate of 5% a year until she retires at the age of 65. She wants to save a fixedpercentage of her income per year. She wants to save enough money to be able to consume per year 50% of her income (in real terms) just before retirement (at age 65) for 20 years. Assume the inflation rate of 3%, and a nominal rate of return on Ann’s savings of 6%. What fraction of income should Ann be saving?

Answer 1

	Years to retirement	39	(65-26)
	Income growth rate=5%	0.05
	Current annual income	$60,000
	Annual Income just before retirement	$402,285	(60000*(1.05^39)
	Amount required per year during retirement	$201,143	(402385*0.5)
	Number of years during retirement	20
	Nominal rate of return	6%
	Inflation Rate	3%
	Real Rate of return=R
	(1+R)=1.06/1.03=	1.029126214
	Real Rate of return=R=	0.029126214
	Real Rate of return=R=	2.91%
	Value of total retirement amount required at age 65	$3,016,812	(Using PV function of excel with Rate=2.91%, Nper=20,Pmt=-211200)
	Total Savings Required in nominal dollar	$3,016,812
	Future value of Saving after 40 years=(Savings )*(1.06^(40-N))
	N=Year of Saving
	If 100% of Income are saved, the totalsavings:
	Income in year 1(from today)	$6,000
	Income in year 2		(60000*1.05)
	Income in year (N+1)=1.05*(Income in year (N))
	N	A	B=A*(1.06^(40-N))
	Year	Saving (100%)	Future Value of savings
	1	$60,000	$582,210.45
	2	$63,000	$576,717.90
	3	$66,150	$571,277.16
	4	$69,458	$565,887.76
	5	$72,930	$560,549.19
	6	$76,577	$555,260.99
	7	$80,406	$550,022.68
	8	$84,426	$544,833.79
	9	$88,647	$539,693.85
	10	$93,080	$534,602.39
	11	$97,734	$529,558.98
	12	$102,620	$524,563.14
	13	$107,751	$519,614.43
	14	$113,139	$514,712.40
	15	$118,796	$509,856.63
	16	$124,736	$505,046.66
	17	$130,972	$500,282.07
	18	$137,521	$495,562.43
	19	$144,397	$490,887.31
	20	$151,617	$486,256.30
	21	$159,198	$481,668.97
	22	$167,158	$477,124.93
	23	$175,516	$472,623.75
	24	$184,291	$468,165.03
	25	$193,506	$463,748.38
	26	$203,181	$459,373.40
	27	$213,340	$455,039.69
	28	$224,007	$450,746.86
	29	$235,208	$446,494.53
	30	$246,968	$442,282.32
	31	$259,317	$438,109.84
	32	$272,282	$433,976.73
	33	$285,896	$429,882.61
	34	$300,191	$425,827.11
	35	$315,201	$421,809.88
	36	$330,961	$417,830.54
	37	$347,509	$413,888.74
	38	$364,884	$409,984.13
	39	$383,129	$406,116.36
	40	$402,285	$402,285.07
		SUM	$19,474,375.35
	Total Future value at 100% Savings	$19,474,375
	Future Value Required at age 65	$3,016,812
	Savings Required	0.15491187	(3016812/19474375)
	Percentage of Savings Required	15.49%