Question

You are planning on saving for retirement. You wish to retire in 40 years, and you would like to withdraw an annual sum each year to live on starting 40 years from today - You have determined that you will need $100,000 to live on (in today’s dollars) - You estimate inflation (cost of living) to be 3% - Your estimated rate of return pre-retirement is 10%; in retirement 7% Assume your life expectancy once retired is another 20 years. How much money do you need to set aside today and for the next 39 years for you to reach your goal? HINT – Use a real rate of return in retirement (growing annuity) – verify your results with a schedule showing payments, income and disbursements

Answer 1

Future value of Annuity invested in retirement fund from year 1 to year 40 = Cash flow per period* Future value annuity factor

= X * ((1+real interest rate)^40-1)/real interest rate = X* (1.07^40)-1)/0.07

Present value of Annuity after retirement from 41 to 60 year = 100000* Present value annuity factor

= 100000*(1-(1.04)^-20)/0.04 = 1359033

by equating FV to PV we have value of annual investment to be $6807.583