Question

You are planning to save for retirement. You would like to retire 25 years from today and you currently have $100,000 set aside. You anticipate saving $420 every other week (26 periods per year – $280 out of your pocket and $140 from a company match) into your 401(k) plan. You anticipating earning an 8.7% rate of return over the next 12 years. After 12 years, you will change your biweekly savings to $X every other week (combined contribution from you and your employer into your 401(k) plan) over the last 13 years of your savings period. During these 13 years, you will lower your risk-return strategy so that the expected return will be 8%. Once you hit retirement, you want to take out $200,000 on the day you retire. After that, you will take out money at the end of each year as follows:

              Years 1-4            $110,000 per year

              Years 5-12          $130,000 per year

              Years 13-25        $120,000 per year

Finally, you want to have $330,000 remaining at the end of the 25-year retirement period and you anticipate earning 4.8% per year in retirement (Hint: Note that the $330,000 remaining is at year 25 of the retirement period so that your year 25 CF is actually $450,000 – the last $120,000 plus the $330,000). Figure out how much you need to save every other week over the final 13 years leading to retirement in order to meet your plan.

Answer 1

		Current Savings	$100,000
		Future value of current savings at the end of 12 years	$            272,116	(100000*((1+0.087)^12)
		Amount of saving per period	$420
		Number of periods in 12 years(26*12)	312
		Interest rate per period=(8.7/26)%
		Future value of bi weekly savings at the end of 12 years	$230,401	(using excel FV function with Rate=(8.7/26)%,Nper=312, Pmt=420)
		Total amount available at the end of 12 years	$            502,517	(230401+272116)
		Future value of this amount($502517) at the time of retirement	$        1,366,657	(502517*(1+0.08)^13)		(Interest rate reduced to 8%)
		CALCULATION OF AMOUNT REQUIRED AT RETIREMENT
		Present Value(PV0 of cash flow=(Cash flow)/(1+i)^N)
		i=interest rate=4.8%=0.048, N= Year of Cash flow
		Year wise cash flow and PV of cash flow are given below:
		N	A	(A/(1.048^N)
		Year	Cash flow	PV of cash flow
		0	$200,000	200000
		1	$110,000	104961.8321
		2	$110,000	100154.4199
		3	$110,000	95567.19457
		4	$110,000	91190.07115
		5	$130,000	102834.0497
		6	$130,000	98124.09323
		7	$130,000	93629.85995
		8	$130,000	89341.46942
		9	$130,000	85249.49372
		10	$130,000	81344.93675
		11	$130,000	77619.21446
		12	$130,000	74064.13594
		13	$120,000	65235.58656
		14	$120,000	62247.69709
		15	$120,000	59396.65753
		16	$120,000	56676.19994
		17	$120,000	54080.34345
		18	$120,000	51603.38116
		19	$120,000	49239.86751
		20	$120,000	46984.60641
		21	$120,000	44832.6397
		22	$120,000	42779.23636
		23	$120,000	40819.88202
		24	$120,000	38950.2691
		25	$450,000	139373.5774
			TOTAL	$       2,046,301
	X	Amount required at the time of retirement for future needs	$        2,046,301
	Y	Amount available from beginning 12 years savings at retirement	$        1,366,657
	Z=X-Y	Amount required to be saved during 13 years	$            679,643
		Number of bi weekly period in 13 years=13*26	338
		Interest rate per period=(8/26)%
	W	Future value of $ 1 saving per period for 13 years	$593.03	( Using excel FV function with Rate=(8/26)%, Nper=338, Pmt=1)
	T=Z/W	Amount of savings required per period	$          1,146.06
		Amount needed to be saved every other week for final 13 years	$          1,146.06