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In: Finance

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

Solutions

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 2 years ago
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