Sammy Slick works for a company that allows him to contribute up to 10% of his...

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	1.305 $ 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	1.198 $ million

d. What do you learn from Sammy's example?
Invest early

Expert Solution


	Current salary	$35,000
	Most likely increase in a year	3.50%
	Salary next year	$36,225	(35000*1.035)
	Salary in year( N+1)=1.035*Salary in Year (N)
	Expected employers match	50%
	Expected annual return on investment	12.5%

	Future Value of Saving after 30 years=(Saving)*(1.125^(30-N))
	N=Year of cash flow

	a. If Sammy contributes 10% of his income to this plan
	N	A	B=A*0.1	C=0.5*B	D=B+C	FV=D*(1.125^(30-N))
Age	Year	Salary	Contribution	Employer match	Total Savings	Future value
30	1	$35,000	$3,500	$1,750	$5,250	$ 159,802
31	2	$36,225	$3,623	$1,811	$5,434	$ 147,018
32	3	$37,493	$3,749	$1,875	$5,624	$ 135,256
33	4	$38,805	$3,881	$1,940	$5,821	$ 124,436
34	5	$40,163	$4,016	$2,008	$6,024	$ 114,481
35	6	$41,569	$4,157	$2,078	$6,235	$ 105,323
36	7	$43,024	$4,302	$2,151	$6,454	$ 96,897
37	8	$44,530	$4,453	$2,226	$6,679	$ 89,145
38	9	$46,088	$4,609	$2,304	$6,913	$ 82,013
39	10	$47,701	$4,770	$2,385	$7,155	$ 75,452
40	11	$49,371	$4,937	$2,469	$7,406	$ 69,416
41	12	$51,099	$5,110	$2,555	$7,665	$ 63,863
42	13	$52,887	$5,289	$2,644	$7,933	$ 58,754
43	14	$54,738	$5,474	$2,737	$8,211	$ 54,054
44	15	$56,654	$5,665	$2,833	$8,498	$ 49,729
45	16	$58,637	$5,864	$2,932	$8,796	$ 45,751
46	17	$60,690	$6,069	$3,034	$9,103	$ 42,091
47	18	$62,814	$6,281	$3,141	$9,422	$ 38,724
48	19	$65,012	$6,501	$3,251	$9,752	$ 35,626
49	20	$67,288	$6,729	$3,364	$10,093	$ 32,776
50	21	$69,643	$6,964	$3,482	$10,446	$ 30,154
51	22	$72,080	$7,208	$3,604	$10,812	$ 27,741
52	23	$74,603	$7,460	$3,730	$11,190	$ 25,522
53	24	$77,214	$7,721	$3,861	$11,582	$ 23,480
54	25	$79,916	$7,992	$3,996	$11,987	$ 21,602
55	26	$82,714	$8,271	$4,136	$12,407	$ 19,874
56	27	$85,609	$8,561	$4,280	$12,841	$ 18,284
57	28	$88,605	$8,860	$4,430	$13,291	$ 16,821
58	29	$91,706	$9,171	$4,585	$13,756	$ 15,475
59	30	$94,916	$9,492	$4,746	$14,237	$ 14,237
					SUM	$ 1,833,796
	Money he could expect to have at age 60	1.834	$million

b	Sammy makes 10% contributions to this plan for eight years, from age 30 to 37,


	N	A	B=A*0.1	C=0.5*B	D=B+C	FV=D*(1.125^(30-N))
Age	Year	Salary	Contribution	Employer match	Total Savings	Future value
30	1	$35,000	$3,500	$1,750	$5,250	$ 159,802
31	2	$36,225	$3,623	$1,811	$5,434	$ 147,018
32	3	$37,493	$3,749	$1,875	$5,624	$ 135,256
33	4	$38,805	$3,881	$1,940	$5,821	$ 124,436
34	5	$40,163	$4,016	$2,008	$6,024	$ 114,481
35	6	$41,569	$4,157	$2,078	$6,235	$ 105,323
36	7	$43,024	$4,302	$2,151	$6,454	$ 96,897
37	8	$44,530	$4,453	$2,226	$6,679	$ 89,145
				SUM	$47,521	$ 972,358
	Total Investment	0.047	$million
	Ending Balance	0.972	$million

	c. Sammy contributes 10% for twenty-three years from age 38 to age 60

	N	A	B=A*0.1	C=0.5*B	D=B+C	FV=D*(1.125^(30-N))
Age	Year	Salary	Contribution	Employer match	Total Savings	Future value
38	9	$46,088	$4,609	$2,304	$6,913	$ 82,013
39	10	$47,701	$4,770	$2,385	$7,155	$ 75,452
40	11	$49,371	$4,937	$2,469	$7,406	$ 69,416
41	12	$51,099	$5,110	$2,555	$7,665	$ 63,863
42	13	$52,887	$5,289	$2,644	$7,933	$ 58,754
43	14	$54,738	$5,474	$2,737	$8,211	$ 54,054
44	15	$56,654	$5,665	$2,833	$8,498	$ 49,729
45	16	$58,637	$5,864	$2,932	$8,796	$ 45,751
46	17	$60,690	$6,069	$3,034	$9,103	$ 42,091
47	18	$62,814	$6,281	$3,141	$9,422	$ 38,724
48	19	$65,012	$6,501	$3,251	$9,752	$ 35,626
49	20	$67,288	$6,729	$3,364	$10,093	$ 32,776
50	21	$69,643	$6,964	$3,482	$10,446	$ 30,154
51	22	$72,080	$7,208	$3,604	$10,812	$ 27,741
52	23	$74,603	$7,460	$3,730	$11,190	$ 25,522
53	24	$77,214	$7,721	$3,861	$11,582	$ 23,480
54	25	$79,916	$7,992	$3,996	$11,987	$ 21,602
55	26	$82,714	$8,271	$4,136	$12,407	$ 19,874
56	27	$85,609	$8,561	$4,280	$12,841	$ 18,284
57	28	$88,605	$8,860	$4,430	$13,291	$ 16,821
58	29	$91,706	$9,171	$4,585	$13,756	$ 15,475
59	30	$94,916	$9,492	$4,746	$14,237	$ 14,237
				SUM	$223,498	$861,438
	Total Investment	0.223	$million
	Ending Balance	0.861	$million

jeff jeffy answered 1 year ago

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