Question

You plan to retire in 29 years. You would like to maintain your current level of consumption which is $59,445 per year. You will need to have 22 years of consumption during your retirement. You can earn 5.55% per year (nominal terms) on your investments. In addition, you expect inflation to be 2.36% inflation per year, from now and through your retirement.

How much do you have to invest each year, starting next year, for 7 years, in nominal terms to just cover your retirement needs?

Answer 1

Real Interest Rate = [(1+Nominal Interest Rate)/(1+Inflation Rate)]-1 = [(1+0.0555)/(1+0.0236)]-1 = 0.0311645

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 59445, i = Interest Rate = 0.0311645, n = Number of Periods = 22

PV at RETIREMENT = 59445*[1-{(1+0.0311645)^-22}]/0.0311645 = 59445*0.49092/0.0311645 = $936412.28

PV of above amount at 7 years from now i.e. before 22 years = FV/[(1+Interest Rate)^Number of Years] = 936412.28/[(1+0.0311645)^22] = 936412.28/1.96433 = $476707.66

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, FV = 476707.66, i = Interest Rate = 0.0311645, n = Number of Periods = 7

Therefore,

476707.66 = P*[{(1+0.0311645)^7}-1]/0.0311645

14856.3559= P*1.23964

Therefore, Amount to be deposited each year = P = 14856.3559/1.23964= $11984.41