Question

I expect to be retired for about 20 years (240 months). I expect to earn 6% APR compounded monthly (after-tax) on my investments during my retirement years and I also expect inflation to average about 1.8% annually (compounded monthly). How much do I need to have saved to be able to spend the equivalent of $10,000 per month during each month of my retirement (note that you will be able to spend $10,000 during the first month of retirement and this amount will increase each month to keep my purchasing power at $10,000 dollars)?

Answer 1

Let the amount of $10000 be required at the beginning of the 1st month of retirement

Monthly inflation rate = 1.8%/12 =0.0015

Monthly interest rate = 6%/12 =0.005

So, Amount required at the time of retirement to spend during all the years of retirement

= Value of 240 amounts at the time of retirement

=10000+10000*1.0015/1.005+10000*1.0015^2/1.005^2+......+ 10000*1.0015^239/1.005^239

From the sum of GP formula

=10000 *(1-(1.0015/1.005)^240)/(1-1.0015/1.005)

=$1,628,425.89

So, for the purpose, one has to save $1628425.89 by the time of retirement