5.1 Assume you have $1 million now, and you have just retired from your job. You expect to live for 20 years, and you want to have the same level of consumption (i.e., purchasing power) for each of these 20 years, after adjusting for inflation. You also wish to leave the purchasing power equivalent of $100,000 today to your kids at the end of the 20 years as a bequest (or to pay them to take care of you).

You expect inflation to be 3% per year for the next 20 years, and nominal interest rates are expected to stay around 8% per year.

ii. If you plan to consume $1.03 in year 1, how much will you need to have to keep the same real consumption in year 2? In year 10? In year 20?

iii. How much, in nominal dollars, will $1 of retirement funds earn in year 1? Year 2? Year 10? Year 20?