You have turned 70 years old. You started saving for retirement at age 35. At the time, you were making $50,000 a year, and your salary was growing by 5% every year. You made annual contributions to your pension savings equal to 10% of your salary each year. For simplicity, let's assume you made your pension contribution on December 31 of each year. You have invested your retirement savings in a mutual fund. Your mutual fund has a beta coefficient of 1.5. Historically (i.e. during the period you saved for retirement) the risk-free rate was constant at 3% and the market excess return was 7%.

A) How much is in your retirement account now? Show the progress of your decision. Be sure to label all inputs that go into calculating annual deductions, including r, g, T, and annual payment amount.

b) You expect to live to age 90, but plan to build up a reserve until age 95, just in case. How much can you spend each year? Let's say you withdraw money once a year and change your investment strategy to a zero beta strategy.

c) Suppose that as a result of excessive consumption of kumiss you develop a serious gastrointestinal disease that leads to death at the age of 80 years. What will be the amount that will be inherited by our children?