Question

Sammy Slick works for a company that allows him to contribute up to 10% of his earnings into a tax-deferred savings plan. The company matches a portion of the contributions its employees make based on the organization's financial performance. Although the minimum match is 25% of the employee's contributions and the maximum match is 100%, in most years the company match is about 50%. Sammy is currently 30 years old and makes $35,000. He wants to retire at age 60. He expects his salary to increase in any given year to be at least 2% per year, at most 6%, and most likely 3.5%. The funds contributed by Sammy and his employer are invested in mutual funds. Sammy expects the annual return on his investments to vary according to a normal distribution with a mean of 12.5% and standard deviation of 2%.

a. If Sammy contributes 10% of his income to this plan, how much money could he expect to have at age 60? Round your answer to three decimal places.
$  million

b. Suppose Sammy makes 10% contributions to this plan for eight years, from age 30 to 37, and then stops contributing. How much of his own money would he have invested and how much money could he expect to have at age 60? Round your answers to three decimal places, if necessary.

Total investment	$ million
Ending balance	$ million

c. Now suppose Sammy contributes nothing to the plan his first eight years and then contributes 10% for twenty-three years from age 38 to age 60. How much of his own money would he have invested and how much money could he expect to have at age 60? Round your answers to three decimal places, if necessary.

Total investment	$ million
Ending balance	$ million

Answer 1

ANSWER;

	Number of years to retire	30	(60-30)
	Current Salary	$35,000
	Next years expected salary	$36,225	(35000*1.035)
	Salary in year (N+1)=1.035*Salary in year( N)
	First years saving	$3,500	(35000*0.1)
	Expected matching contribution by the company	$1,750	(3500*0.5)
	Mean return from investment=12.5%	0.125
	Future Value(FV) of Savings=(Savings)*((1+i)^(30-N))
	i=expected return from investment=0.125
	N=Year of Saving
	Year wise Saving and FV of savings are given below
A	N	A	B=A*0.1	C=0.5*B	D=B+C	E=D*((1.125^(30-N)
	Year	Expected Salary	Expected Saving	Expected Match	Total Saving	FV of Total Saving
	1	$35,000	$3,500	$1,750	$5,250	159802.0898
	2	$36,225	$3,623	$1,811	$5,434	147017.9226
	3	$37,493	$3,749	$1,875	$5,624	135256.4888
	4	$38,805	$3,881	$1,940	$5,821	124435.9697
	5	$40,163	$4,016	$2,008	$6,024	114481.0921
	6	$41,569	$4,157	$2,078	$6,235	105322.6047
	7	$43,024	$4,302	$2,151	$6,454	96896.79636
	8	$44,530	$4,453	$2,226	$6,679	89145.05265
	9	$46,088	$4,609	$2,304	$6,913	82013.44844
	10	$47,701	$4,770	$2,385	$7,155	75452.37256
	11	$49,371	$4,937	$2,469	$7,406	69416.18276
	12	$51,099	$5,110	$2,555	$7,665	63862.88814
	13	$52,887	$5,289	$2,644	$7,933	58753.85708
	14	$54,738	$5,474	$2,737	$8,211	54053.54852
	15	$56,654	$5,665	$2,833	$8,498	49729.26464
	16	$58,637	$5,864	$2,932	$8,796	45750.92347
	17	$60,690	$6,069	$3,034	$9,103	42090.84959
	18	$62,814	$6,281	$3,141	$9,422	38723.58162
	19	$65,012	$6,501	$3,251	$9,752	35625.69509
	20	$67,288	$6,729	$3,364	$10,093	32775.63948
	21	$69,643	$6,964	$3,482	$10,446	30153.58833
	22	$72,080	$7,208	$3,604	$10,812	27741.30126
	23	$74,603	$7,460	$3,730	$11,190	25521.99716
	24	$77,214	$7,721	$3,861	$11,582	23480.23739
	25	$79,916	$7,992	$3,996	$11,987	21601.8184
	26	$82,714	$8,271	$4,136	$12,407	19873.67292
	27	$85,609	$8,561	$4,280	$12,841	18283.77909
	28	$88,605	$8,860	$4,430	$13,291	16821.07676
	29	$91,706	$9,171	$4,585	$13,756	15475.39062
	30	$94,916	$9,492	$4,746	$14,237	14237.35937
					SUM	1833796.489
	Sammy is expected to have at the age of 60	$ 1,833,796.49
	Sammy is expected to have at the age of 60	$1.834	million
B	If Sammy has contributed for 8 years from 30 to 37 years
	N	A	B=A*0.1	C=0.5*B	D=B+C	E=D*((1.125^(30-N)
	Year	Expected Salary	Expected Saving	Expected Match	Total Saving	FV of Total Saving
	1	$35,000	$3,500	$1,750	$5,250	159802.0898
	2	$36,225	$3,623	$1,811	$5,434	147017.9226
	3	$37,493	$3,749	$1,875	$5,624	135256.4888
	4	$38,805	$3,881	$1,940	$5,821	124435.9697
	5	$40,163	$4,016	$2,008	$6,024	114481.0921
	6	$41,569	$4,157	$2,078	$6,235	105322.6047
	7	$43,024	$4,302	$2,151	$6,454	96896.79636
	8	$44,530	$4,453	$2,226	$6,679	89145.05265
		SUM	$31,681		SUM	$972,358
	Total Investment (his own money)	$31,681
	Ending Balance	$972,358
	Total Investment (his own money)	$0.032	million
	Ending Balance	$0.972	million
C	If Sammy has contributed only for 23 years from 38 to 60 years
	N	A	B=A*0.1	C=0.5*B	D=B+C	E=D*((1.125^(30-N)
	Year	Expected Salary	Expected Saving	Expected Match	Total Saving	FV of Total Saving
	9	$46,088	$4,609	$2,304	$6,913	82013.44844
	10	$47,701	$4,770	$2,385	$7,155	75452.37256
	11	$49,371	$4,937	$2,469	$7,406	69416.18276
	12	$51,099	$5,110	$2,555	$7,665	63862.88814
	13	$52,887	$5,289	$2,644	$7,933	58753.85708
	14	$54,738	$5,474	$2,737	$8,211	54053.54852
	15	$56,654	$5,665	$2,833	$8,498	49729.26464
	16	$58,637	$5,864	$2,932	$8,796	45750.92347
	17	$60,690	$6,069	$3,034	$9,103	42090.84959
	18	$62,814	$6,281	$3,141	$9,422	38723.58162
	19	$65,012	$6,501	$3,251	$9,752	35625.69509
	20	$67,288	$6,729	$3,364	$10,093	32775.63948
	21	$69,643	$6,964	$3,482	$10,446	30153.58833
	22	$72,080	$7,208	$3,604	$10,812	27741.30126
	23	$74,603	$7,460	$3,730	$11,190	25521.99716
	24	$77,214	$7,721	$3,861	$11,582	23480.23739
	25	$79,916	$7,992	$3,996	$11,987	21601.8184
	26	$82,714	$8,271	$4,136	$12,407	19873.67292
	27	$85,609	$8,561	$4,280	$12,841	18283.77909
	28	$88,605	$8,860	$4,430	$13,291	16821.07676
	29	$91,706	$9,171	$4,585	$13,756	15475.39062
	30	$94,916	$9,492	$4,746	$14,237	14237.35937
		SUM	$148,998		SUM	$861,438
	Total Investment (his own money)	$148,998
	Ending Balance	$861,438
	Total Investment (his own money)	$0.149	million
	Ending Balance	$0.861	million

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