. An engineer has the option of retiring and collecting social security when he

ID: 1141249 • Letter: #

Question

. An engineer has the option of retiring and collecting social security when he is 62, 66.5, or 70 years old. If he decides to start his social security income at age 62 or 66.5, he will only be entitled to a reduced amount rather than the entire amount he would receive if he retires at age 70. Table I contains the amounts the engineer would receive on a monthly basis for each of the three different Table 1. Social Security Monthly Payments by Starting Age Monthly Income Age 62 66.5 70 $2,412 $3,151 A. If the engineer estimates he will live to be 85 years old, what would be the present value for each of the social security age alternatives assuming the interest rate is 4%? Assuming that maximizing the present value of social security payments is his only criterion, when should the engineer retire? B. what would be the present value of the three starting age alternatives if the engineer only lives to 77 years old? When should he retire in this case? [Use of Excel is encouraged for this question, but you must show one example calculation in detail)

Explanation / Answer

Age of Retirement

Monthly Income ($)

Annual Income ($)

Period for A (Years)

Period for B (Years)

PV for A ($)

PV for B ($)

1799

21588

8758.82

11987.05

66.5

2412

28944

15.5

10.5

15759.48

19173.81

3151

37812

23617.26

28734.01

Here A represents the case where he lives until 85 years of age. Here, if he retires at 62 then the period for A = 23 years.

Similarly, B represents the case where he lives until 77 years of age. Here, if he retires at 62 then the period for B = 15 years.

The formula for Present Value (PV) = Future Value/ (Discount Rate)

Or PV = FV/(1+i)^n

Where Discount Rate = (1+i)^n such that i = 4% (0.04) here and n refers to the period for which pension is valid.

Therefore PV for A when he retires at 62 is: 21588/(1+0.04)^23

A) In this case, the engineer should retire when he’s 70 years old with the highest PV of $23617.26

B) In this case too, the engineer should retire when he’s 70 years old with the highest PV of $28734.01