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

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 607 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 Ending balance c. Now suppose Sammy contributes nothing to the plan his first eight years and then contributes 10% for twe ree ear from age 8to age . 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 Ending balance d. What do you learn from Sammy's example? million million million million Select

Explanation / 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 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 to37 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 23years from 38 to60years 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 d FV of first eight years savings is higher than FV of savings of 23 years at later period This shows the power of compoinding of returns More the time given for compounding, higher will be the return

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