Reference no: EM132901739

Consumption Smoothing and Retirement.

Part A) Suppose you want to retire at age 60 and plan until age 90. You have a constant real consumption equal to $4,000 per month until death and you are earning $6,000 (real) per month that remains constant until retirement. Find the time in which your human capital becomes equal to your financial capital if the real valuation rate is 3.54% (APR).

Part B) Suppose you are 65 years old, recently retired, and have $500,000 saved in a retirement savings account earning a guaranteed rate of return of 3.0357% (APR) per year. You are entitled to a Defined Benefit (DB) pension of $48,000 per year, paid monthly. You can either start your pension now or when you become 70 years old (it is NOT possible to start pension anytime between 65 and 70). But, once you pull the trigger and start the pension, it remains fixed and constant at that level. If you wait to start your pension at age 70, you will receive a bonus of 7.2% (APR) for every year you wait (5*7.2% = 36% more in total). Find the month t such that if you live exactly until that month, you would be indifferent between starting your pension at 65 and 70 years old. If you die after month t, you would be better off starting pension at age 70. If you die before month t, you would be better off starting pension at age 65.