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my 401k by age equation
Old 04-23-2012, 03:17 PM   #1
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my 401k by age equation

While trying to find a good answer for "how much should I have saved for retirement at age X?" I came to a few conclusions:

1) Most Americans are way under on saving for retirement (so using averages as a benchmark is a BAD idea).

2) It depends on what you make. Someone living a life in the salary range of $300-500K isn't going to be very happy retiring on only $80,000 a year... but the average American at the $50K salary range would be living large on the same amount.

3) It depends on when you want to retire. As is the theme of this board... if you plan to retire early... you need a variable to tweak for speeding up the process.

Taking into account 1 & 2 I came across a novel concept that retirement progress should be a factor of both age and salary. In fact, age itself isn't a good one, but rather how long you'd been in the workforce. The simple equations that say subtract x from your age and multiple by salary... fall apart for someone in their 20's or 30's.

Assuming most workers start in the early to mid 20's its not unreasonable to set a path towards retirement on an assumption of a 35-40 year working career.

So here it is... RET ACCOUNT = ([2^(Y/7)] - 1) * Current Salary
Y = number of years working

(a lot easier than it looks when you break it apart)
Basically all this means is that you should have double your salary after you've been working 7 years and you should expect to roughly double that ratio of savings to salary every 7 years after that

So, someone making $50,000 a year that has been in the workforce for 10 years should have [2^(10/7)-1]*50K or $84,000 in their retirement. If they are making $70,000 when they've been in 25 years, their account should then be[2^(25/7)-1]*70K = $761,000.

The number SEVEN turns out to be a great factor to use in our equations for two reasons. Historically speaking, a 10% return in equities means that money invested over a really long time should just about double every 7 years. 1.10^7 = 1.95 (ok ok, so some decades you'll see less then that, but others you'll see more - we're talking 30-40 years total, whats the average going to be?). The fact that you're still contributing to it makes up the slack...

On this path your retirement account should be the following factors of your salary at the following working ages:

7 years on job = 1x salary
14 years on job = 3x salary
21 years on job = 7x salary
28 years on job = 15x salary
35 years on job = 31x salary (why are you still working !)

Obviously... if you follow this model there isn't much of a point to working much past 35 years (or even 33 years) because you'll have enough in retirement to hit the magic 4% rule where you can now withdraw your salary from your retirement account each year.

This also doesn't account for the fact that you probably don't need as much to live on in retirement as your working years... so you can adjust accordingly (maybe lower Current Salary to be 80% of Current Salary as you get closer to Retirement)

Also please note that it assumes you want to be 100% dependent on your 401K... in reality, you'll have SS and possibly a pension or house paid off to pad things even more for you. Factor those in accordingly.

You can also tweak this equation more by setting the number 7 to be larger or smaller. If you need more years working till retirement you might want to try using 8 instead, if you want to FIRE you could try fitting in 6 instead.

In fact, the best place to start is decide how long you wish to work... then fit it into this equation to come up with the number you should use in place of 7 in the equation: Years Working / 4.65

So if you want to retire after working for 30 years and plan for SS to account for 25% of your retirement spending, your value is 30/4.65 = 6.45 and your equation should be:

RET ACCOUNT = ([2^(Y/6.45)] - 1) * (Current Salary - 25%)

where Y = years you've been working. We've introduced the -25% to current salary to show how you can account for 25% coming from SS.

Like all the others... not perfect, but it is really simple and you can compute your target account value any time (even using fractions of a year working)... You can also change the equation itself based on changes in your life...

Anyone else have equations they've either come across or created themselves to help set milestones for retirement account savings?
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Old 04-24-2012, 02:36 PM   #2
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I assume you mean: (( 2^(Y/6.45) ) - 1) * (Current Salary - Current Salary*.25) or RET ACCOUNT = (( 2^(Y/6.45) ) - 1) * (Current Salary*.75)

Anyways, cool idea. By your equation I'm right on due to aggressive savings, however when I started working at age 15 I was making $50 a week!

Thanks!!
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Old 04-24-2012, 03:12 PM   #3
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When I was planning for retirement, I came up with "net worth goals" as a function of annual expenses.

Age 35 NW=6 x annual expenses
Age 40 NW=11 x annual expenses
Age 45 NW=17 x annual expenses
Age 50 NW=24 x annual expenses
Age 55 NW=32 x annual expenses

I started working at age 27.

Pretty close to your results, maybe a tad more aggressive.

Why not calculate our net worth goals as a function of income? Because our income increased so fast that income-based formulas always made it look like we were falling behind. Income-based formulas may work well for people with stable incomes, but they did not work well for us. Our expenses, on the other end, have been much more stable over time and I thought they made for a better measuring stick.

Finally, the assumption that people with high incomes could not happily retire on modest incomes, while probably valid for the general population, undoubtedly breaks down with the FIRE crowd.
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Old 04-24-2012, 03:13 PM   #4
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Finally, the assumption that people with high incomes could not happily retire on modest incomes, while valid for the general population, probably breaks down with the FIRE crowd.
Particularly this. When someone is a prodigious saver -- and I think we have more than our share here -- chances are they will have living expenses that are much lower than their incomes.
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Old 04-24-2012, 04:43 PM   #5
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Originally Posted by FIREd View Post
Why not calculate our net worth goals as a function of income? Because our income increased so fast that income-based formulas always made it look like we were falling behind. Income-based formulas may work well for people with stable incomes, but they did not work well for us. Our expenses, on the other end, have been much more stable over time and I thought they made for a better measuring stick.
Good point. This works a lot better for someone in a very stable and reliable job sector (like a software engineer). The goal was to have a way to look at my progress towards retirement... getting to that magic 20-25x salary mark.

Obviously, having an understanding of how these numbers all work and what they mean is required. Example: I'd never turn down a 100% raise... thinking it would extend retirement plans 12 years according to my equation .

As a person nears retirement and has a better sense of their goal for retirement spending, it makes more sense to substitute in EXPECTED SPENDING IN RETIREMENT in place of CURRENT SALARY
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Old 04-24-2012, 06:18 PM   #6
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Good point. This works a lot better for someone in a very stable and reliable job sector (like a software engineer). The goal was to have a way to look at my progress towards retirement... getting to that magic 20-25x salary mark.
Actually, there is nothing magic about that 20-25x number. For example, someone making $400K and living on $80K might only need to hit the 5-7x salary mark. Someone making $100K and living on $50K might only need to hit the 12-17x salary mark. Savings rates matter.

The "magic" number - if there is such a thing- is 25-33x your expected annual expenses in retirement. Granted, it may be hard to estimate how much you will spend in 20-30 years, but your current spending pattern could give you clues. If you still prefer to use your salary as reference, then you must incorporate your savings rate in the equation.
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