John is deciding between two possible retirement options that will benefit both him and his wife. According to the mortality tables, his life expectancy is 83 years (conditional that he survived to the present age). Life expectance of his wife, Emma is 87 years (conditional that she survived to the present age). Emma is 3 years younger than John. John considers two retirement options. The question is which retirement option will result is higher Social Security Retirement Benefits.
Option 1. John will retire at the age of 62 and will receive a yearly social security benefit of $20,000 for himself. His wife will get 50% of his retirement benefit ($10,000 per year).
Option 2. John will retire at the age of 69 and will receive a yearly social security benefit of $40,000 for himself. His wife will get 50% of his retirement benefit ($20,000 per year).
Calculate the present value of social security benefits for the family for both options. Present value should be calculated at the time when John is 63 years old. Compare these two options using present values. Use a yearly interest rate of 3%, for both options. Use life expectancy values (i.e., consider that John will die when he is 83 years old and his wife will die when she is 87 years old).
Consider simplifying assuptions:
John and Emma will get only one cash flow in the end of every calendar year. E.g., if John retires when he is 62 years old, than he gets the first cash flow, $20,000, in the end of this year and Emma gets $10,000 at the same time as John, when she is 59 years old (62-3 = 59).
John will get the last cash flow in the end of the year when he is 83 years old, and Emma will get the last cash flow in the end of the year when she is 87 years old.