Question

You plan to retire in 23 years. You would like to maintain your current level of consumption which is $51,594 per year. You will need to have 29 years of consumption during your retirement. You can earn 5.27% per year (nominal terms) on your investments. In addition, you expect inflation to be 2.06% 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 nominal terms to just cover your retirement needs?

Answer 1

Given, I am planning to retire in 23 years and I maintain my current consumption level at $51,594 per year whereas the inflation rate remains at 2.06%.

Therefore, Future Value of my consumption level per year after 23 years will be= $[51594(1+0.0206%)^23] =$82,466.4256

So, the total consumption for 29 years of my retirement, after 23 years, along with 2.06% inflation

= $82,466.4256[{(1+0.0206)^29}-1]÷ 0.0206

=$82466.4256[1.80638932-1]÷0.0206

=$3,228,157.52

So the future value of my total investments for next 10 years should be atleast = $3,228,157.52

Since, given that, I can earn 5.27% per year in nominal terms on my investment.

The amount of investment that should made each year for next 10 years starting from next year , can be calculated as follows-

Let the amount of annual investment(annuity) be $P.

We get-

P[{(1+0.0527)^10}-1]÷0.0527 = 3,228,157.52

P[(1.67126851-1]÷0.0527=3,228,157.52

P[0.67126851÷0.0527]= 3,228,157.52

P[12.7375429]=3,228,157.52

P=3,228,157.52÷12.7375429

P=253,436.399

Thus, my annual investment each year for the next 10years should be= $253,436.399 in nominal terms to cover my retirement needs.