Question

You plan to retire in 21 years. You would like to maintain your current level of consumption which is $38,591 per year. You will need to have 25 years of consumption during your retirement. You can earn 5.6% per year (nominal terms) on your investments. In addition, you expect inflation to be 4.32% 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 real terms to just cover your retirement needs?

Answer 1

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

= ((1+0.056) / (1+ 0.0432)) -1

= 1.23%

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 = 1.23%

n is the no of compounding period 25 years

=

= 826213.31

Now this amount is required in 21 years but we are only investing for 7 years therefore value of 826213.31 after 7 years from today is = Future Value / (1+r)^n

r = 0.0123

n = (21-7) = 14 years

= 826213.31 / (1+0.0123)^14

= 696246.25

Now 696246.25 is required after 7 years. This is the future value of Annuity

696246.25 =

r = 0.0123

n = 7

696246.25 =

696246.25 = Periodic Payment * 7.26366076016

Periodic Payment = 95853.38

WE need to deposit 95853.38 every year for 7 years.