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

Amount needed during each month of the retirement which will be equivalent with the purchasing power of the withdrawal amount of first month = $10,000

Calculating the amount need to be saved using Present value of Growing Ordinary annuity formula:-

Where, C= First month withdrawal amount = $10,000

r = Periodic Interest rate = 6%/12 = 0.5%

g = growth rate of annuity = 1.8%/12 = 0.15%

n= no of periods = 240 months

Present Value = $1,620,324.26

So, amount needs to be saved for retirement is $1,620,324.26