Saturday, June 30, 2012

How much money will I need to retire?

Geek alert:  this post has math in it.  A lot of math.  Can't help myself.  But I love it.

At my college reunion last month, I got to hear some of my former classmates talk about retirement savings strategies.  IRAs, Roth, Index funds, blah blah blah.  That's all important, of course -- I don't mean it's not.  But it wasn't THE NUMBER.  There was lots of talk about how to get to enough, but not any mention of how to figure out how much IS enough.  Am I putting the right amount of money into my retirement accounts?  Or, since I'm probably not going to change my retirement contributions much anyway, how much money am I looking at if I keep going as-is?

Isn't that what we all really wonder?  If I keep going as I'm going, what will the future look like?  Can I handle that, or do I need to change?

Some people doodle pictures.  I doodle math.  So when my attention wandered, I decided to try to figure out a formula to estimate, in broad terms, what THE NUMBER will be, to predict the future based on the past and the present.  I should caution that "estimate" is key here, because there are a gazillion variables in real life -- I'm not looking for perfection, just for a rough idea.

To get a handle on this, I decided to pretend I know 5 things for sure (and obviously, I don't know them all).  Here's what I pretended I know:  1) S,  how much I've already saved, 2) D for "deposit", that is, how much I'll contribute to savings in each year of the future years, 3) Y, the number of years before I retire, 4) r, average interest rates between now and then, and 5) w, my eventual withdrawal rates.

If by some stroke of luck I manage to nail each of those five numbers exactly on the head, then when I retire my monthly withdrawal from my retirement account will be what you get from this beautiful formula:
monthly retirement income = [ S*R + (R-1)*D/r ] * w/12.

Now, why couldn't they have showed us that formula during the talk?
Okay, maybe I know why.

Do you hate math yet?  Or are you like me and are chomping at the bit?  

If you're not a fan of algebra but you want to figure out how to do this computation with your own numbers, here's a step-by-step set of instructions with fake numbers tossed in. Only 6 steps, and the first is the hardest.
  1. Guess the average rate of return on my investments before I retire -- little r.  This is a huge guess here.  As a matter of fact, I ran the formula a bunch of times with a bunch of numbers, all centered around 0.08.  Then compute the total return, R, by using your guessed interest (r) and years to retirement (Y), using the formula R = (1+r)^Y. That ^ symbol means multiply by itself that many times -- most calculators have that button. If yours doesn't, just hit 1.08, "times", and then hit the "=" button for as many years as you expect to be working.  If I will work for 20 more years, that's R=(1.08)^20=4.66.
  2. Figure out how much your current savings will be worth in Y years:  that's S*R (your current savings times your total rate of return).  If I've saved $25,000, that'd be 25,000*4.66, or $116,500.
  3. Figure out how much your future deposits will earn:  Subtract 1 from R; multiply that number by your annual deposit D, and divide by the interest rate r.  If I deposit $100/month or $1200/year, I'd do 3.66*1200 (that's 4392), and then divide that by 0.08, to get $54,900.
  4. Add the numbers from steps 2 and 3.  That's how much money you'll have in your retirement account when you're ready to retire.   (Continuing, I'd get 116,500 + 54,900, or $171,400).
  5. Figure out your yearly withdrawal rate by multiplying step 4 by w (in my example, 171,400*0.04 = $6,856).
  6. Figure out your monthly withdrawal by dividing step 5 by 12.  (With those numbers, I'd be living on 6,856/12 = $571 per month). 
I figured it makes sense to compare that number from step 6 to how much money we actually spend now -- again, this is all for broad estimation purposes.  If I decided this number was too low (and I'm guessing living on $571 a month is too low, really), I have options -- I could wait longer to retire (change Y).  I could save more money (change D).  I could try to get a better interest rate (change r and therefore R).   Or I could invent a time machine, go back in time, and save more money up to now (change S).   Well, okay, maybe not that.

If this formula is more than you want to deal with, you can find other retirement calculators online.  Most of them tell you how much you should be setting aside now, not how much spending money you'll have eventually if you keep going as you're going now.  But they all do the calculations for you.  Where's the fun in that?

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