5. (25 points) According to the Social Security Administration, a 62 year old American man is expected to live to age 82. Suppose a 67 year old is expected to live to the same age. Consider an individual who is 62 years old, with an AIME of $3,200. For the year 2020, the two "bend points in the PIA formula are at $960 and $5,785. Every dollar of AIME below the first bend point translates to 90 cents of PIA; every dollar of AIME between the bend points translates to 32 cents of PIA; and every dollar of AIME above the second bend point translates to 15 cents of PIA. (a) Supposing this person's AIME won't change if they work 5 more years, what monthly benefit would they receive if they retired at 67? (b) Calculate what the monthly benefit should be if this person retires at age 62, in order to keep the expected total amount of money they receive the same (don't worry about trying to discount future time periods). (C) Suppose this person has a family history of longevity, and so they expect to live to age 90. Using the early benefit payment you found in part (a), should they retire at age 62 or age 67? (d) Suppose this person has a family history of early death, and they only expect to live to age 75. Using the early benefit payment you found in part (a), should they retire at age 62 or age 67? (e) Actually, a 67 year old American male is expected to live to be 83.5, not 82. How does this change the above analysis? (Hint: if a 62 year old expects to live to be 90, should they have the same expectation when they're 67?) 5. (25 points) According to the Social Security Administration, a 62 year old American man is expected to live to age 82. Suppose a 67 year old is expected to live to the same age. Consider an individual who is 62 years old, with an AIME of $3,200. For the year 2020, the two "bend points in the PIA formula are at $960 and $5,785. Every dollar of AIME below the first bend point translates to 90 cents of PIA; every dollar of AIME between the bend points translates to 32 cents of PIA; and every dollar of AIME above the second bend point translates to 15 cents of PIA. (a) Supposing this person's AIME won't change if they work 5 more years, what monthly benefit would they receive if they retired at 67? (b) Calculate what the monthly benefit should be if this person retires at age 62, in order to keep the expected total amount of money they receive the same (don't worry about trying to discount future time periods). (C) Suppose this person has a family history of longevity, and so they expect to live to age 90. Using the early benefit payment you found in part (a), should they retire at age 62 or age 67? (d) Suppose this person has a family history of early death, and they only expect to live to age 75. Using the early benefit payment you found in part (a), should they retire at age 62 or age 67? (e) Actually, a 67 year old American male is expected to live to be 83.5, not 82. How does this change the above analysis? (Hint: if a 62 year old expects to live to be 90, should they have the same expectation when they're 67?)
