Part A) Suppose you want to retire at age 65 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 (assuming that you don’t have any pension). Find the time (i.e., age) in which your human capital becomes equal to your financial capital if the real valuation rate is 3.306% (APR). Assume that there are no implicit and explicit liabilities.

Part B) Imagine that you are entitled to receive a pension at age 65 (the amount of the pension does not change the answer. You can assume it to be $X or any other number you prefer). You can delay triggering the pension to age 70, but as a result, you would be entitled to receive a bonus of 7.2% (APR) for every year you wait (5*7.2% = 36% more in total). So, if you start it at age 70, you can receive 1.36 times the amount you would receive if you start it at age 65. Assume that it is NOT possible to start pension anytime between 65 and 70 (only two options of 65 or 70). Find the time/age t such that if you live exactly until that time, you would be indifferent between starting your pension at 65 and 70 years old. If you die after time t, you would be better off starting pension at age 70. If you die before time t, you would be better off starting a  pension at age 65. The valuation rate is 3.0357% (APR) per year.