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Save $700/mo, Retire In 40 Yrs on $16k/mo

One of the classes I’ve been taking involves investing, discounting cash flows, blah blah; and so one of the things we’ve touched upon is retirement savings. One of our recent problems is calculating how much you need to save in during pre-retirement in order to guarantee (based on assumptions) a future cash flow. So, rather than study the textbook and answer problems with very little payoff (yeah yeah, I have a test), I figured I’d create my own problem and submit it to you all to see if I did it correctly.

Q. How much do I have to save each month for the next forty years in order to ensure that I can withdraw $5,000 a month, in 2007 dollars, for the next twenty years?

Assumption #1: No taxes. 🙂
Assumption #2: Inflation will be 3% a year for the next 40 years.

Given that assumption, $5,000 in purchasing power in 2007 will be $16,310 in 2047, so you’ll need to have enough retirement assets such that you can withdraw $16,310 each month ($195,720 a year) for the next 25 years. In order to calculate that amount, you’ll need to know the rate of return on your assets during those 25 years, as you draw it down.

Assumption #3: Your post-retirement assets will appreciate at 5% a year.

At 5% a year and drawing out $288,060 a year, you’ll need assets in the amount of $3,848,183 in Year 40. That means between now and year 40, you’ll need to save and appreciate nearly four million dollars in order to retire on $5,000 a month (2007 dollars) for the next 25 years. (if that seems a little high, it’s because you have to discount your rate of return by inflation each year) Scary huh?

So, how much do you need to save? Let’s hit up assumption 4…

Assumption #4: Your pre-retirement investments will appreciate at 10%.

Now, in order to have $3,848,183 in retirement assets in 40 years, how much will you need to save each month if your savings appreciate at 10% each year? (This time we don’t discount for inflation because it’s already taken into account by the payout each month) It’s actually quite reasonable, a mere $8,694.54 a year… or $724.55 a month.

(Someone please check my math!)