Consider the retirement choice of a 69-year-old worker who expects to live until
ID: 1151992 • Letter: C
Question
Consider the retirement choice of a 69-year-old worker who expects to live until age 74. If she retires at age 69, she will receive $19,500 per year in Social Security benefits for the remaining five years of her life. If she delays her retirement until age 70, she will receive $22,500 per year in Social Security benefits for the remaining four years of her life. In addition, she will earn $25,000 this year at her job.
What is the discounted present value of her lifetime earnings if she
(i) retires at age 69 and (ii) delays retirement until age 70, assuming a discount rate of 3 percent?
Explanation / Answer
Consider the retirement choice of a 69-year-old worker who expects to live until age 74.
If she retires at age 69, she will receive $19,500 per year in Social Security benefits for the remaining five years of her life.
If she delays her retirement until age 70, she will receive $22,500 per year in Social Security benefits for the remaining four years of her life.
In addition, she will earn $25,000 this year at her job.
What is the discounted present value of her lifetime earnings if she
(i) Retires at age 69
Present Value = $19,500 (P/A, 3%, 5)
Present Value = $19,500 (4.5797)
Present Value =89,304
(ii) delays retirement until age 70, assuming a discount rate of 3 percent?
He receives on 70th year = $25,000
Remaining 4 years = $22,500 per year
Present Value (at 70th year) = $25,000 + $22,500 (P/A, 3%, 4)
Present Value (at 70th year) = $25,000 + $22,500 (3.7171)
Present Value (at 70th year) = 108,635
If we calculate Present value at 69th year
Present Value = 108,635 (P/F, 3%, 1)
Present Value = 108,635 (0.9709) = 105,474