Question

Assume 360-day year and 30-day month in your analysis Salary scalar 3.33 Your clients, both just turned 40, will retire when they turn 62. They have a current salary at an annual rate of ($10,000*salary scalar + $100,000), being paid equally at the end of each month. They expect a 3% raise in their salary every year until they retire. They deposit 12% of their monthly salary in their 401(k) account that generates an annual rate of return of 10%, compounded daily. In addition, their employer matches their contribution with 5% of their monthly salary to the same 401(k) account. 1. Determine the cash flows pattern of the monthly contributions to the 401(k) account within each year; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate the yearend value of the 401(k) contributions for each year. Verify your work for Years 1 and 2 only with either the formula or the financial calculator approach! 2. Determine the pattern of the year-end values of the 401(k) contributions across years; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate their 401(k) account balance upon their retirement.

Answer 1

	Current Annual Salary	$133,300	(10000*3.33+100000)			133300
	Next years Annual Salary	$137,299	(133300*1.03)
	Salaty in year (n+1)=1.03*Salary in year(n)
	Interest rate:
	10% compounded daily
	Effective annual Rate=r
	(1+r)=(1+(0.1/365))^365
	1+r=	1.105155782
	r=	0.105155782
	Monthly rate=i
	(1+i)^12=1.105155782
	1+i=(1.105155782^(1/12))=	1.008367001
	Monthly interest rate =i=	0.008367001					(Using Excel FV Function with
	Number of years of savings	22	(62-40)				Rate=0.008367001,
							Nper=12,Pmt=E
	N	A	B=A/12	C=B*0.12	D=B*0.05	E=C+D	F	G=F*(1.105155782^(22-N))
	Year	Annual Salary	Monthly Salary	Deposit in 401(k)	Employer	Total	Year End Value	Value of Yearly
					Match	Savings		Saving at retirement
	1	$133,300	$11,108	$1,333	$555	$1,888	$23,733.46	$                                   193,756
	2	$137,299	$11,442	$1,373	$572	$1,945	$24,445.47	$                                   180,579
	3	$141,418	$11,785	$1,414	$589	$2,003	$25,178.83	$                                   168,299
	4	$145,661	$12,138	$1,457	$607	$2,064	$25,934.20	$                                   156,854
	5	$150,030	$12,503	$1,500	$625	$2,125	$26,712.22	$                                   146,187
	6	$154,531	$12,878	$1,545	$644	$2,189	$27,513.59	$                                   136,246
	7	$159,167	$13,264	$1,592	$663	$2,255	$28,339.00	$                                   126,980
	8	$163,942	$13,662	$1,639	$683	$2,323	$29,189.17	$                                   118,345
	9	$168,860	$14,072	$1,689	$704	$2,392	$30,064.84	$                                   110,297
	10	$173,926	$14,494	$1,739	$725	$2,464	$30,966.79	$                                   102,796
	11	$179,144	$14,929	$1,791	$746	$2,538	$31,895.79	$                                     95,806
	12	$184,518	$15,377	$1,845	$769	$2,614	$32,852.67	$                                     89,291
	13	$190,054	$15,838	$1,901	$792	$2,692	$33,838.25	$                                     83,218
	14	$195,756	$16,313	$1,958	$816	$2,773	$34,853.39	$                                     77,559
	15	$201,628	$16,802	$2,016	$840	$2,856	$35,898.99	$                                     72,285
	16	$207,677	$17,306	$2,077	$865	$2,942	$36,975.96	$                                     67,369
	17	$213,907	$17,826	$2,139	$891	$3,030	$38,085.24	$                                     62,788
	18	$220,325	$18,360	$2,203	$918	$3,121	$39,227.80	$                                     58,518
	19	$226,934	$18,911	$2,269	$946	$3,215	$40,404.63	$                                     54,538
	20	$233,742	$19,479	$2,337	$974	$3,311	$41,616.77	$                                     50,829
	21	$240,755	$20,063	$2,408	$1,003	$3,411	$42,865.28	$                                     47,373
	22	$247,977	$20,665	$2,480	$1,033	$3,513	$44,151.24	$                                     44,151
							SUM	$                               2,244,066
	Total Amount at retirement	$                      2,244,066