Question

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.

   A.   Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.

       i.   How much do you need for your kids? (180,611.12??)

       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?

       iv.   In an Excel spreadsheet (or in a manual table), calculate the following:

           a.   annual investment earnings for each year

           b.   total savings after investment earnings for each year

           c.   subtract annual consumption from total savings each year

           d.   by trial and error, or with the Goal Seek command, determine the amount of consumption that will give you exactly $100,000, in today's purchasing power, at the end of 20 years

Hint: You will need to make your annual consumption column dependent on the inflation rate, your investment earnings will grow at the nominal rate, and the bequest of $100,000 will grow at the inflation rate.

Answer 1

A. Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.

	Total Amount = $1000000
Amount left for Kids in todays equivalent = $100000
Total Amount for Consumption = 900000
Now, as per the formula of present value of growing annuity
900000 = Value/(.08-.03) * (1-(1.03/1.08)^20)
Value = 900000/12.25 = $73469.38
so yearly consumption (real) = $73469.38

i. How much do you need for your kids?

Value = 100000*1.03^20 = $180611.12

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?

Year No.	inflation rate	Amount to be kept
1	3%	1.03
2	3%	1.06
10	3%	1.34
20	3%	1.81

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

Year no.	Interest rate	Earning
1	8%	1.08
2	8%	1.17
10	8%	2.16
20	8%	4.66