1. (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $48,000 per year at the end of each year starting 30 years from now (i.e., the first payment is in time 30), what is the present value of your retirement plan if the discount rate is 5%?

(b) How does your answer to part (a) change if you receive $4,000 per month every month forever (in perpetuity) starting 30 years from today (in monthly time period 360) and you compound monthly?

2. 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) $800 per month for life

II. Regular retirement (Age 66 years, 2 months) $1,000 per month for life

III. Delayed retirement (Age 70 exactly) $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))