Author Topic: Shockingly Simple Math Question  (Read 2226 times)

alcon835

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Shockingly Simple Math Question
« on: May 25, 2019, 08:05:02 AM »
Okay, there is one thing I'm struggling with. I make a sizable income and am using it to invest heavily and also save for things like future rental properties, taking care of family, etc.

However, I'd like to retire at some point and live off of significantly less income than I'm making now. The calculators I find online don't seem to account for this very well. So here is my questions around the shockingly simple math:

If I want to live off of $65,000/yr, then I need to invest 64% of that number ($41,600/yr) for 10.6 years in order to hit that number, right?

It really shouldn't matter how much money I'm making today as long as I plan to live off of the 65K number in the future.

Am I off base, or do my numbers add up?

FLOW

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Re: Shockingly Simple Math Question
« Reply #1 on: May 25, 2019, 08:15:10 AM »
Define your terms.  You want to live off 65K until you die?  What assumptions are you making for investment returns?  For inflation? 

You might find this helpful: https://www.investor.gov/additional-resources/free-financial-planning-tools/compound-interest-calculator

Mad Fientist has this: https://lab.madfientist.com

There's also things like FireCalc (?)...

Shockingly Simple Math is a simple, aspirational document; it's more Declaration of Independence than some cookbook you can follow line by line. 

FLOW

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Re: Shockingly Simple Math Question
« Reply #2 on: May 25, 2019, 08:27:33 AM »
Or.... if you're really just looking for a simple guideline, then... you want your future monthly expense X 300.  *

If you want to have a portfolio that generates 65K per year, then you need a portfolio in today's dollars of 1.625million

Here's how I got that: 65K divided by 12 is 5,416 per month. 

5416 X 300 is 1,625,000

That might be more what you're looking for, I think.

*I honestly can't remember what assumptions underlie this estimate.  MMM has a post on it somewhere.  I think it's 4% real returns on the portfolio.

MDM

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Re: Shockingly Simple Math Question
« Reply #3 on: May 25, 2019, 03:08:53 PM »
*I honestly can't remember what assumptions underlie this estimate.  MMM has a post on it somewhere.  I think it's 4% real returns on the portfolio.
It's the 4%/yr withdrawal rate suggested by historical data.  This is not the same as assuming 4% returns, either real or nominal.

See
http://www.retailinvestor.org/pdf/Bengen1.pdf
http://www.aaii.com/files/pdf/6794_retirement-savings-choosing-a-withdrawal-rate-that-is-sustainable.pdf
https://www.bogleheads.org/wiki/Trinity_study_update
https://www.bogleheads.org/wiki/Safe_withdrawal_rates
for some reading.

TomTX

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Re: Shockingly Simple Math Question
« Reply #4 on: May 25, 2019, 07:33:00 PM »

If I want to live off of $65,000/yr, then I need to invest 64% of that number ($41,600/yr) for 10.6 years in order to hit that number, right?

Saying "10.6 years" is over-precision. The timeframe will depend in large part on what the stock market does in the meantime. On average, it would be 10.6 years, but it's unlikely to end up exactly that number.

alcon835

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Re: Shockingly Simple Math Question
« Reply #5 on: May 26, 2019, 08:14:11 AM »
I think I asked the question poorly.

I want my withdrawal rate at retirement of 4% to be $65,000. This, presumably, takes into account yearly 2-3% inflation (which is my current assumption). To get there, I would need $1,625,000 in total investments. According to the Shockingly Simple Math, I should be able to achieve that in ~10 years as long as I'm putting away ~$42,000/yr in investments over those 10 years.

Obviously, nothing is perfect and who knows what the market will do. But based on the Shockingly Simple Math that is more-or-less the idea behind the whole thing.

The problem I'm running into in all of the FIRE calculators is they ask for my current income. When I put that number in, I get a wildly different outcome that says it will take a really long time for me to get to that goal. It seems like all those calculators assumes I'm going to live at my current lifestyle and income level into retirement.

So, to clarify my question: Regardless of my income, if I want to withdraw $65,000/yr in FIRE retirement, assuming a 4% withdrawal rate, I should be bale to hit that number in ~10 years as long as I invest 64% of $65,000 (aka $~42,000/yr). This also assumed I am investing in pretty standard index funds for that time.

Am I understanding the math correctly, or to live off of $65,000 in the future do I need to be investing 64% of my current income? It seems like my assumptions above are correct, but almost none of the calculators seem to account for what I'm trying to math out.

the_gastropod

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Re: Shockingly Simple Math Question
« Reply #6 on: May 26, 2019, 08:32:39 AM »
No no no. I think youíve misunderstood the shockingly simple math post a little bit. First, yes, the assumption in the math is that, in retirement, youíll spend the same as you do while working.

Your income matters in this calculation only because itís the denominator used for calculating your savings rate. The interesting part of the shockingly simple math is that given your savings rate, you can forecast how long youíll need to work.

In your example, saving $42,000 for 10 years (at a 5% interest rate) you wonít come anywhere near $1.6 million. Youíll only have ~500k at that point. Saving 64% of your salary today will get you to retirement in about 10 years.

I hope that helps.

FLOW

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Re: Shockingly Simple Math Question
« Reply #7 on: May 26, 2019, 08:39:35 AM »
Have you tried out literally any of the calculators we provided in this thread? 

You've already been provided multiple calculators to help you estimate that.  I've provided you with 2 of them.  And neither is hamstrung by the problems you're describing.

Tell you what -- just give me the numbers and I'll get you an estimate.  You're trying to figure out how long it will take to save up 1.625 million?  Fine. 

How much investment money do you have right now? (I'm going to assume you're investing ALL of it)
How much are you able to save each month?  (I'm going to assume you're going to invest everything you're saving)
What interest rate should we assume for your investments over this time period?




FIREstache

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Re: Shockingly Simple Math Question
« Reply #8 on: May 26, 2019, 09:13:35 AM »
*I honestly can't remember what assumptions underlie this estimate.  MMM has a post on it somewhere.  I think it's 4% real returns on the portfolio.
It's the 4%/yr withdrawal rate suggested by historical data.  This is not the same as assuming 4% returns, either real or nominal.

See
http://www.retailinvestor.org/pdf/Bengen1.pdf
http://www.aaii.com/files/pdf/6794_retirement-savings-choosing-a-withdrawal-rate-that-is-sustainable.pdf
https://www.bogleheads.org/wiki/Trinity_study_update
https://www.bogleheads.org/wiki/Safe_withdrawal_rates
for some reading.

Here's another good one:

https://www.kitces.com/wp-content/uploads/2014/11/Kitces-Report-March-2012-20-Years-Of-Safe-Withdrawal-Rate-Research.pdf

teen persuasion

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Re: Shockingly Simple Math Question
« Reply #9 on: May 26, 2019, 09:58:38 AM »
I think I asked the question poorly.

I want my withdrawal rate at retirement of 4% to be $65,000. This, presumably, takes into account yearly 2-3% inflation (which is my current assumption). To get there, I would need $1,625,000 in total investments. According to the Shockingly Simple Math, I should be able to achieve that in ~10 years as long as I'm putting away ~$42,000/yr in investments over those 10 years.

Obviously, nothing is perfect and who knows what the market will do. But based on the Shockingly Simple Math that is more-or-less the idea behind the whole thing.

The problem I'm running into in all of the FIRE calculators is they ask for my current income. When I put that number in, I get a wildly different outcome that says it will take a really long time for me to get to that goal. It seems like all those calculators assumes I'm going to live at my current lifestyle and income level into retirement.

So, to clarify my question: Regardless of my income, if I want to withdraw $65,000/yr in FIRE retirement, assuming a 4% withdrawal rate, I should be bale to hit that number in ~10 years as long as I invest 64% of $65,000 (aka $~42,000/yr). This also assumed I am investing in pretty standard index funds for that time.

Am I understanding the math correctly, or to live off of $65,000 in the future do I need to be investing 64% of my current income? It seems like my assumptions above are correct, but almost none of the calculators seem to account for what I'm trying to math out.
You've misunderstood the variables.

To reach FIRE in 10.x years, you need to save 64% of your income, not 64% of your desired expenses.  It's assumed the other 36% of income is your expenses.

So if income is $100k, savings rate is 64% ($64k), expenses are $36k.

MDM

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Re: Shockingly Simple Math Question
« Reply #10 on: May 26, 2019, 09:59:44 AM »
So, to clarify my question: Regardless of my income, if I want to withdraw $65,000/yr in FIRE retirement, assuming a 4% withdrawal rate, I should be be able to hit that number in ~10 years as long as I invest 64% of $65,000 (aka $~42,000/yr). This also assumed I am investing in pretty standard index funds for that time.
Highly unlikely, unless you already have a significant amount invested.

For $42K/yr to reach $1,625K in 10.6 years takes an investment return of 21% or more.

You might find How to use the Excel FV function helpful.

dandarc

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Re: Shockingly Simple Math Question
« Reply #11 on: May 26, 2019, 10:07:00 AM »
Good catch teen persuasion and MDM.

Shockingly simple math post is how long to get to retirement at an XX% savings rate starting from 0. Starting from 0 is a big assumption - people start down this path from a wide spectrum of net worth.

For your standard W-2 employee without a defined-benefit pension plan, savings rate is

(after-tax income + retirement contributions - expenses) / (after-tax income + retirement contributions)

It is important to keep in mind the time to retirement is just an estimate based on somewhat conservative historical stock market returns. Actual results will vary depending on many factors.

jeroly

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Re: Shockingly Simple Math Question
« Reply #12 on: May 26, 2019, 10:32:44 AM »
Following up on teen persuasion's post..
If you want to have your spending be $65k/year, and to reach FI in 10.9 years, you'd need that to map to a 64% savings rate.

In other words, $65k would correspond to 36% of your income, which implies an income of $65000/.36= $181,556 of which you save $116,556 (64%) and spend $65,000 (36%).


 

secondcor521

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Re: Shockingly Simple Math Question
« Reply #13 on: May 26, 2019, 11:06:55 AM »
It sounds to me like OP makes more than that, but wants to plan to live on $65K and retire in about 10.6 years.

OP, yes, it will approximately work if you invest the 64% of that number and the stock market returns as assumed, AND you cut back your spending in 10.6 years to that $65K.

If you're currently making more and only investing the $41.6K, then you must be dispensing of the excess somehow.  In 10.6 years, you wouldn't be able to.  That will be a lifestyle adjustment of some kind for you.

Generally the assumption that you spend in retirement about what you're spending before you retire is based on the idea that most people are accustomed to living at a certain level and that changing that level - especially downward - is tough.  (Changing it upward is challenging too, but in a different way to which most are unsympathetic.)  If that is your plan - to downsize your expenses when you retire - then I would highly recommend that you have a rock-solid logical bulletproof reason for the reduction.

Peachtea

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Re: Shockingly Simple Math Question
« Reply #14 on: May 26, 2019, 12:19:11 PM »
OP just use a basic compound interest calculator to calculate dollar amount you need to save in x years to get your 1,625,000 stache needed for 65k a year at 4%. If youíre starting with zero and assume 7% average returns, you would need to invest 100k a year to have 1,625,000 in (a little over) 10.7 years.

http://www.moneychimp.com/calculator/compound_interest_calculator.htm


alcon835

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Re: Shockingly Simple Math Question
« Reply #15 on: May 26, 2019, 02:20:08 PM »
Okay, there have been a few folks in here who I think cleared it up for me.

The 64% is not taken from the amount you'll be living on in retirement, instead the 36% is the amount I'd be living on in retirement (in this case $65,000). So for me to get to the point where I can withdrawal 65K/yr in retirement, i need to invest more like 115K/yr as that would equal to 64% if 65K were 36%.

That makes sense and clears up some confusion I had around the calculators.

FLOW

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Re: Shockingly Simple Math Question
« Reply #16 on: May 26, 2019, 04:04:48 PM »
If your expenses now are going to be very different than your expenses in retirement, then the Shockingly Simple Math savings rate grid isn't the best tool for the financial questions you're trying to answer. This whole thread was like watching someone use a can opener to hammer a nail into the wall...

In theory, if you started with zero and made $162,500,000 post-tax in the next year, and saved only 1% of it, you'd hit your number.  That's right -- you'd hit your number, in just one year, with a 1% savings rate. 

 

BTDretire

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Re: Shockingly Simple Math Question
« Reply #17 on: May 27, 2019, 10:38:19 AM »
Also beware of the inflation cost, using 3% inflation, $65k in 10.6 years is like living on $47.5K today.
So, I suggest you live on $47.5k of you sizable income and see if you can do that.
 We are testing ourselves this year with $50k, and It looks like we will overspend.
I will admit we had some extenuating circumstances, so even if we over spend, I will try the same number again,
with an inflation adjustment.

sol

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Re: Shockingly Simple Math Question
« Reply #18 on: May 27, 2019, 11:17:02 AM »
If your expenses now are going to be very different than your expenses in retirement, then the Shockingly Simple Math savings rate grid isn't the best tool for the financial questions you're trying to answer.

Agreed.  The shockingly simple math approach is for people who have current expenses that are well below their income, and intend to spend that same amount of (inflation adjusted) money on expenses into the future.

Example:  Starting from zero, if you make 100k/year and spend $36k/year, then your savings rate is 64% because you're investing 64k out of 100k.  You should be able to retire in 10.9 years if the stock market provides historically average returns, because in 10.9 years your $64k/year of annual investments will compound to 25 times 36k, or $900k.  900k should be sufficient to support your 36k of expenses for at least 30 years, based on the 4% rule of thumb.

But there is another great tool that allows you to calculate the time needed to save up to an arbitrary savings goal based on assumed market returns and specific dollar contributions.  It's called a spreadsheet, and I firmly believe that nobody should attempt early retirement without a firm grasp of how to use one.  Each person's situation is unique, and all of these web tools are necessarily simplified versions of your real life plan.  You need to plot out your own real life plan, in a way that you fully understand and appreciate, before pulling the trigger on RE.  I don't think any of the simplified web tools can provide that for you.