Question

You plan to retire in 24 years. You would like to maintain your current level of consumption which is $30,471 per year. You will need to have 24 years of consumption during your retirement. You can earn 6.67% per year (nominal terms) on your investments. In addition, you expect inflation to be 4.33% inflation per year, from now and through your retirement. How much do you have to invest each year, starting next year, for 8 years, in real terms to just cover your retirement needs?

Answer 1

Yearly Annual Consumption required after 24 years (at the age of retirement)

$30,471 x (1.0433)²⁴ x 12 = $1,011,320.78

We have to calculate the return after adjusting the inflation using the below formula

((1+r)/(1+i)-1) x 100

Where r is the rate of return earned on investments after retirement

i is the inflation rate.

Inflation adjusted rate of return would using the above formula will be (1.0667/1.0433 - 1) x 100 = 2.243%

The corpus required at the time of retirement will be calculated as the future value annuity factor for 2.243% for 24 years.

The future value annuity factor is calculated using FV annuity factor table as 16.2361

So annual corpus required is 16.2361 x $1,011,320.78 = $16,419,885.43

The amount which needs to be invested for 8 years starting next year would be calculated as below

Calculated using the Present value annuity factor for 8 years which is calculated as below

1/1.0667 + 1/(1.0667)² + 1/(1.0667)³ + ..... + 1/(1.0667)⁸ = 6.04842

Therefore the amount to be invested is calculated below as

$16,419,885.43 6.04842 = $2,714,739.6229