3. A family friend is retiring from work in the U.S. She is exactly 62 years old

Question

3. A family friend is retiring from work in the U.S. She is exactly 62 years old right now (time 0) and has the choice of taking her Social Security (a public pension program) right now or delaying according to the following schedule: I. Early retirement (Age 62 exactly) 11. Regular retirement (Age 66 years, 2 months) III. Delayed retirement (Age 70 exactly) $800 per month for life $1,000 per month for life $1,240 per month for life If her expected life expectancy is 80 years old (exactly), what are the present values of the choices? (Assume r-6% (annual))

Explanation / Answer

Present value of annuity = Annuity [1- (1+r)-n] / r where n = No. of periods, r = rate per period

or PV = Annuity * PV factor for n periods

We will use PV factors.

1. Early retirement = 800 * 19.999 = $15999.2

(PV factor for 0.5% interest per month for 216 months)

2. Regular retirement = 1000 * 19.993 = $19993

  (PV factor for 0.5% interest per month for 166 months)

3. Delayed retirement = 1240 * 19.9426 = $24728.824

(PV factor for 0.5% interest per month for 120 months)

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