Question

You plan to retire in 22 years. You would like to maintain your current level of consumption which is $52,558 per year. You will need to have 34 years of consumption during your retirement. You can earn 4.4% per year (nominal terms) on your investments. In addition, you expect inflation to be 2.09% inflation per year, from now and through your retirement.

How much do you have to invest each year, starting next year, for 12 years, in nominal terms to just cover your retirement needs?

Answer 1

Real Interest Rate(after adjusting Inflation) = [(1+Nominal Interest Rate)/(1+Inflation Rate)]-1 = [(1+0.044)/(1+0.0209)]-1 = 1.022627-1 = 0.022627= 2.2627%

Balance required at the beginning of retirement i.e. 22 years from now = PV of Annuity

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

Where, P = Annuity = 52558, i = Interest Rate = 0.022627, n = Number of Periods = 34

PV = 52558*[1-{(1+0.022627)^-34}]/0.022627= 52558*0.53268/0.022627= $1237311.81

Balance required at 12 years from now = PV of above amount before 10 years = FV/[(1+Interest Rate)^Numer of Years = 1237311.81/[(1+0.022627)^10] = 1237311.81/1.25076 = $989251.25

Amount to be deposited every year = Annuity for FV of $989251.25

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

Where, FV = 989251.25, i = Interest Rate = 0.022627, n = Number of Periods = 12

989251.25= P*[{(1+0.022627)^12}-1]/0.022627

22383.79= P*0.308

Therefore, P = 22383.79/0.308= $72675.13

Therefore, Amount to be deposited each year for 12 years = $72675.13