Question

I expect to be retired for about 18 years (216 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 2.4% 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 the $10,000 will increase each month to keep my purchasing power at $10,000 in today's dollars)?

Answer 1

Interest rate per month =6%/12 = 0.5% or 0.005

Inflation rate per month = 2.4%/12 =0.2% or 0.002

No of months = 18*12 = 216

Assuming that $10000 is required at the beginning of the 1st month and thereafter the amounts will increase at the rate of 0.2% every month

Savings required ($)

= 10000 +10000*1.002/1.005 + 10000*1.002^2/1.005^2+......+10000*1.002^215/1.005^215

=10000*(1-(1.002/1.005)^216)/(1-1.002/1.005)

=$1593681.33

(In case 1st amount of $10000*1.002 is required at the end of the month,

Savings required = $1593681.33*1.002/1.005 = $1588924.07)