Question

In: Finance

You plan to retire in 21 years. You would like to maintain yourcurrent level of...

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?

Solutions

Expert Solution

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.


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