Question

You plan to retire in 22 years. You would like to maintain your current level of consumption which is $49,971 per year. You will need to have 26 years of consumption during your retirement. You can earn 5.82% per year (nominal terms) on your investments. In addition, you expect inflation to be 3.95% inflation per year, from now and through your retirement.

How much do you have to invest each year, starting next year, for 10 years, in real terms to just cover your retirement needs?

Answer 1

Real Rate of Return = ((1+Nominal Return) / (1+ Inflation)) -1

= ((1+0.0582) / (1+ 0.0395)) -1

= 1.80%

Value required at the begnning of the retirement = Present Value of Annuity

Present Value Annuity =

where r is the rate of Return for compounding period = 1.80%

n is the no of compounding period 26 years

=

= 1,030,331.2188

Now this amount is required in 22 years but we are only investing for 10 years therefore value of 1,030,331.2188 after 10 years from today is = Future Value / (1+r)^n

r = 0.018

n = (22-10) = 12 years

= 1,030,331.2188 / (1+0.0180)^12

= 831,770.518418

Now 831,770.518418 is required after 10 years. This is the future value of Annuity

831,770.518418 =

r = 0.0180

n = 10

831,770.518418 =

831,770.518418 = Periodic Payment * 10.8501315727

Periodic Payment = 76659.95

WE need to deposit 76659.95 every year for 10 years.