Question

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.

Q1. 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!

Q2. 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. Verify your work with the formula approach!

At the end of each year, your clients will receive a bonus of 15% of their annual salary. Your clients commit to deposit part of their annual bonus, $14,000, in a 529 Plan account each year for financing their daughter’s, who just turned 12, college education. They will keep contributing to the 529 account until their daughter finishes college. Any remaining amount from the annual bonus check will be deposited in an IRA account. The 529 Plan account and the IRA account are expected to generate annual rates of return of 8% and 10%, respectively. And both accounts are compounded daily.

Q3. Determine the cash flows pattern of their contributions to the IRA account; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate their IRA account balance upon their retirement.

Q4. Determine the cash flows pattern of their contributions to the 529 Plan account; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate the 529 Plan account balances at the time their child starts college. Verify your work with either the formula or the financial calculator approach!

Currently, annual college expenses are running at $30,000, and are expected to grow at an annual rate of 5%. Their daughter will enter college when she turns 18, and complete the degree program in five years. Your clients expect their daughter to be responsible for 30% of her college expenses via the work-study program. All annual college expenses will be due at the beginning of each year. Your clients will tap into the 529 Plan account for paying their daughter’s college expenses.

Q5. Will there be sufficient funding in the 529 account for financing their daughter’s college expenses? If not, when will the funding run out of money? Support your answer numerically by showing the annual balances of the 529 Plan account through their daughter’s college years.

With a positive balance in the 529 account at their daughter’s college graduation, your clients will partially support her graduate study with money left in the 529 account. Their daughter plans to work for three years before returning to graduate school for an MBA. Currently, annual expenses for a highly competitive full-time 2-year MBA program are running at $55,000, and are expected to grow at an annual rate of 4%. Your clients will offer assistance to their daughter’s pursuit of graduate education through the 529 account at one-third of the annual expenses during her MBA study.

Q6. Will there be sufficient funding in the 529 account for subsidizing their daughter’s MBA program’s expenses? If not, when will the funding run out of money? Support your answer numerically numerically by showing the annual balances of the 529 Plan account through her MBA study.

If there is money left (i.e., positive balance) in the 529 account after their daughter’s MBA study, your client will transfer the balance to their IRA account.

Q7. How large will be the nest egg upon the retirement of your clients? In other words, calculate the combined balance of the 401(k) account and their IRA account when they retire.

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 monthly	Year End Value	Value of Yearly
					Match	Savings		Saving at retirement
	1	$133,300	$11,108	$1,333	$555	$1,888	$23,728.23	193713.02
	2	$137,299	$11,442	$1,373	$572	$1,945	$24,444.60	180573.0474
	3	$141,418	$11,785	$1,414	$589	$2,003	$25,173.54	168263.8303
	4	$145,661	$12,138	$1,457	$607	$2,064	$25,940.18	156890.2714
	5	$150,030	$12,503	$1,500	$625	$2,125	$26,706.82	146157.7186
	6	$154,531	$12,878	$1,545	$644	$2,189	$27,511.17	136233.8664
	7	$159,167	$13,264	$1,592	$663	$2,255	$28,340.65	126987.9075
	8	$163,942	$13,662	$1,639	$683	$2,323	$29,195.27	118369.968
	9	$168,860	$14,072	$1,689	$704	$2,392	$30,062.46	110288.4405
	10	$173,926	$14,494	$1,739	$725	$2,464	$30,967.35	102798.3215
	11	$179,144	$14,929	$1,791	$746	$2,538	$31,897.37	95810.57305
	12	$184,518	$15,377	$1,845	$769	$2,614	$32,852.54	89290.22206
	13	$190,054	$15,838	$1,901	$792	$2,692	$33,832.83	83205.08626
	14	$195,756	$16,313	$1,958	$816	$2,773	$34,850.83	77553.4619
	15	$201,628	$16,802	$2,016	$840	$2,856	$35,893.97	72274.65418
	16	$207,677	$17,306	$2,077	$865	$2,942	$36,974.81	67366.96583
	17	$213,907	$17,826	$2,139	$891	$3,030	$38,080.79	62780.30877
	18	$220,325	$18,360	$2,203	$918	$3,121	$39,224.47	58512.82783
	19	$226,934	$18,911	$2,269	$946	$3,215	$40,405.85	54539.95757
	20	$233,742	$19,479	$2,337	$974	$3,311	$41,612.37	50824.07685
	21	$240,755	$20,063	$2,408	$1,003	$3,411	$42,869.17	47377.10697
	22	$247,977	$20,665	$2,480	$1,033	$3,513	$44,151.09	44151.09384
							SUM	2243962.727
	Total Amount at retirement	$     2,243,962.73