Charles is a senior engineer who has worked for 18 years since he graduated from
ID: 2773169 • Letter: C
Question
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 earn 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 of 8% 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.
The report 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 & 2. Calculation of the total future worth:
Normal retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 * 12 = 18000
19
41.44626
$ 18,000.00
$746,032.74
(Years after retirement till death = 85 -66 =19 Years)
Early retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 *(1-25%)* 12 = 18000
23
60.89330
$ 13,500.00
$822,059.49
(Years after retirement till death = 85 -62 =23 Years)
Extended retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 *(1+30%)* 12 = 18000
15
27.15211
$ 23,400.00
$635,359.47
(Years after retirement till death = 85 -70 =15 Years)
3. Calculation of Present worth of money received by his wife:
Years
PVF (8%)
Cash Flow (CF)
PV = PVF *CF
Present value of Annual Cash Flow after Death = 1600*12 = 19200
19
9.60360
$ 19,200.00
$184,389.10
(Years = 85 years -66years = 19 years )
Present value of the benefits (At the age of 40)
26
0.54027
$184,389.10
$ 99,619.70
(Years = 66 - 40 = 26)
4. Calculation of Future value of money received by his wife:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Future value of Annual Cash Flow after Death = 1600*12 = 19200
19
41.44626
$ 19,200.00
$795,768.25
(Years = 85 years -66years = 19 years )
1 & 2. Calculation of the total future worth:
Normal retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 * 12 = 18000
19
41.44626
$ 18,000.00
$746,032.74
(Years after retirement till death = 85 -66 =19 Years)
Early retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 *(1-25%)* 12 = 18000
23
60.89330
$ 13,500.00
$822,059.49
(Years after retirement till death = 85 -62 =23 Years)
Extended retirement:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Yearly cash flow = 1500 *(1+30%)* 12 = 18000
15
27.15211
$ 23,400.00
$635,359.47
(Years after retirement till death = 85 -70 =15 Years)
3. Calculation of Present worth of money received by his wife:
Years
PVF (8%)
Cash Flow (CF)
PV = PVF *CF
Present value of Annual Cash Flow after Death = 1600*12 = 19200
19
9.60360
$ 19,200.00
$184,389.10
(Years = 85 years -66years = 19 years )
Present value of the benefits (At the age of 40)
26
0.54027
$184,389.10
$ 99,619.70
(Years = 66 - 40 = 26)
4. Calculation of Future value of money received by his wife:
Years
FVF (8%)
Cash Flow (CF)
FV = FVF *CF
Future value of Annual Cash Flow after Death = 1600*12 = 19200
19
41.44626
$ 19,200.00
$795,768.25
(Years = 85 years -66years = 19 years )