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Charles is a senior engineer who has worked for 18 years since he graduated from college. Yesterday in the mail, he received a report from the U.S. Social Security Administration. In short, it stated that if he continues to earm at the same rate, social security will provide him with the following estimated monthly retirement benefits: Normal retirement at age 66; full benefit of $1500 per month starting at age 66. Early retirement at age 62; benefit reduced by 25% starting at age 62. Extended retirement at age 70; benefit increased by 30% starting at age 70. : * Charles never thought much about social security; he usually thought of it as a monthly deduction from his paycheck that helped pay for his parents' retirement benefits from social security. But this time he decided an analysis should be performed. Charles decided to neglect the effect of the following over time: income taxes, cost-of-living increases, and inflation. Also, he assumed the retirement benefits are all received at the end of each year, that is, no compounding effect occurs during the year. Using an expected rate of return on investments of8% per year and an anticipated death Just after his 85th birthday, calculate the following for Charles: 1. Calculate the total future worth of each benefit scenario through the age of 85 2. Plot the annual accumulated future worth for each benefit scenario through the age of 85 also mentioned that if Charles dies this year, his spouse is eligible at full retirement age for a benefit of $1600 per month for the remainder of her life. If Charles and his wife are both 40 years old today, determine the following about his wife's survivor benefits, if she starts at age 66 and lives through her 85th birthday 3. Present worth now 4. Future worth for his wife after her 85th birthday

Explanation / Answer

1.

(a) No compounding occurs during the year. So receiving $1500 every month of year is equivalent to receiving $18000 at the end of that year. So we can think of this cash flow as starting at the end of year 66. The last cash flow is to be received at the end of year 84 (that is, his 85th birthday). So this cash flow has 19 end-of-year inflows, each worth $18000. Calculate the future worth using the uniform series compound amount factor.

            F = 18000 (F/A, 8%, 19)

            = 18000 × 41.446

            = $746028

(b) The benefit now is 1125 per month. No compounding occurs during the year. So receiving $1125 every month of year is equivalent to receiving $13500 at the end of that year. So we can think of this cash flow as starting at the end of year 62. The last cash flow is to be received at the end of year 84 (that is, his 85th birthday). So this cash flow has 23 end-of-year inflows, each worth $13500. Calculate the future worth using the uniform series compound amount factor.

            F = 13500 (F/A, 8%, 23)

            = 13500 × 60.893

            = $822,055.5

(c) The benefit now is 1950 per month. No compounding occurs during the year. So receiving $1950 every month of year is equivalent to receiving $23400 at the end of that year. So we can think of this cash flow as starting at the end of year 70. The last cash flow is to be received at the end of year 84 (that is, his 85th birthday). So this cash flow has 15 end-of-year inflows, each worth $23400. Calculate the future worth using the uniform series compound amount factor.

            F = 23400 (F/A, 8%, 15)

            = 23400 × 27.152

            = $635,356.8

2.

Accumulated worth calculated at the end of year 84 should match our answers in part 1. But due to rounding off, they may differ a little.

(a) The accumulated worth at the end of year 66 is $18000. Calculate the accumulated worth for the end of each other year t as follows.

Accumulated worth at the end of year t

            = [(accumulated worth at the end of year t1)×1.08] + $18,000

Plot the calculated values as follows.

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