You are planning for your retirement in 30 years. At that time you want to have enough saved to be able to afford to spend $100,000 per year (starting at time 31) for 20 years (if you live longer than 20 years your kids will have to support you).
a. How much will you need to have saved by time 30 if the expected interest rate from time 30 to 50 is 10 percent per year?
b. Suppose that at time 30 you will receive a retirement bonus of $50,000 from your company. If the interest rate is expected to be 12 percent, compounded monthly, from now until time 30, how much would you need to save at the end of each month in order to be able to make the desired withdrawals at retirement?