Sammy Slick works for a company that allows him to contribute up to 10% of his e
ID: 2616387 • Letter: S
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.
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.
d. What do you learn from Sammy's example?
Invest early
Explanation / Answer
$million
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
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.