1. Your parents are about to retire and they have $1,000,000 with which to do so. They plan to live 25 more years after retirement. They expect to earn 5% per year, which compounds monthly, on this money. How much money can they withdraw from this total each month and have a 0 balance at the end of 25 years?
2. In problem #1, the rate of interest is a nominal rate. If your parents expect the rate of inflation to average 3% per year for the 25 years, what is the purchasing power of the money they withdraw each year? Again, assume the balance (or FV) at the end of year 25 is $0. (To solve this, use the real interest rate r, which is found by rearranging the Fisher equation of i = r + p , where i is the nominal rate, r the real rate, and p the inflation rate).
3. Problem #2 gives a simplistic view of the problem of "inflation risk," as seen in the inflation premium of the Fisher Equation. Now, recalculate the purchasing power of your parents' retirement income (i.e., standard of living) using a simple sensitivity test. Assume that the inflation rate cannot be accurately predicted, but can range anywhere from 2% to 4% per year. Assume the nominal interest rate remains constant at 5% per year. By how much can your parents' standard of living vary based on inflationary expectations?
4. Explain the significance of each component of the Fisher equation as they relate to the time value of money. How do changes in any of these components cause change in the relationship of present value to future value. You can consider the Fisher equation to be i = r + p + rp, where i is the nominal rate, r the real rate, and p the inflation rate, and rp is the risk premium.