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1.Â Â Â Â Â Your parents are about to retire and they have $1,000,000 with which to do so.Â They plan to live 25 more years after retirement.Â They expect to earn 5% per year, which compounds monthly, on this money.Â How much money can they withdraw from this total *each month* and have a 0 balance at the end of 25 years?

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2.Â Â Â Â Â Assume you have a child who is currently 10 years old.Â You realize that you must begin saving for her college education, and sit down to work out a plan of action.Â You plan to make annual payments, starting at the end of the current year, into an account that earns 5% interest per year.Â When your child begins college, you will put the money into an account that earns 3% interest per year.Â Your child will begin college in 8 years.Â Assume that each year of college will cost $20,000, and (for simplicity) assume this amount must be paid at the beginning of the school year.Â You are planning to pay for five years of college for your child.Â How much money will you need to save each year from now until your child starts college? (Hint: it might be helpful to diagram this problem with a timeline before solving it).

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3.Â Â Â Â Â 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?Â Again, assume the balance (or FV) at the end of year 25 is $0.Â Â (To solve this, use the real interest rate r, which is found by rearranging the Fisher equation of iÂ =Â rÂ +Â pÂ , where i is the nominal rate, r the real rate, and p the inflation rate).

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4.Â Â Â Â Â Problem #3 gives a simplistic view of the problem of Ã¢inflation risk,Ã¢ as seen in the inflation premium of the Fisher Equation.Â Now, recalculate the purchasing power of your parentsÃ¢ retirement income (i.e., standard of living) using a simple sensitivity test.Â Assume that the inflation rate cannot be accurately predicted, but can range anywhere from 2% to 4% per year.Â Assume the nominal interest rate remains constant at 5% per year.Â By how much can your parentsÃ¢ standard of living vary based on inflationary expectations?Â

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5.Â Â Â Â Â Explain the significance of each component of the Fisher equation as they relate to the time value of money.Â How do changes in any of these components cause change in the relationship of present value to future value. Â 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.Â

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