After graduating with a Bachelor of Business Administration degree at age of 22 (i.e., your 22nd birthday), you start working at a private equity firm. Your monthly salary is $5,000 in the first year and increases 4% every year until you retire at 65 (i.e., $6,240 per month in the second year). In each month, you spend 95% of your salary and invest the remaining in a portfolio that earns 12% return per year. On the first day of your retirement, you liquidate your portfolio and deposit the proceeds in a bank account that earns 6% interest per year compounded monthly. You withdraw $X per month at the beginning of each month (Yes, you withdraw the first $X on the day you make the deposit) to pay bills. You want to donate $5,000,000 to UTSC when you die at 85.

a) What is the value of your portfolio when you retire at 65?

b) Find the maximum value of X so that you have enough money to make the donation.