Shockingly Simple Math

[LauraMo]

Is there a reverse formula out there to the Shockingly Simple Math formula?

If we want to retire in X years I would like it to solve for the amount we壇 need to save monthly so we know how much more money we would need to make.

For example, we want our portfolio to provide $45k a year ($45k x 25 = $1.125m). Using the same 5% how do we calculate we壇 need To contribute X in order to retire in 10 years, or maybe we壇 want to retire in 7 years, how much harder would we have to work?

Thanks!

[MDM]

See the 'Misc. calcs' tab in the case study spreadsheet.

[Michael_db97531]

https://www.domestic-engineering.com/fire/01mathbehind_fi/math_FI.html

Here is a complete derivation of the formula approximated the Shockingly Simple Math article.  At the bottom is the formula you want, saving rate as a function of rate of return,  rate of withdrawal, and saving time. Calculate the required saving rate and then since you know you want $45k coming in from investments, calculate I = E/(1-S).    The formula on that page also allows you to start with your current savings, you don't have to assume you have a net worth of $0. 

[ontheway2]

You can just use a simple savings calculator. Put the years quite a bit out, enter your current investments, and play with different savings amounts to see at what point you cross your desired threshold. Remember to use a real rate of return if the calculator doesn't account for inflation

http://www.math.com/students/calculators/source/compound.htm

[JMS]

Is the investment return (say 5%) assumed to be after tax ?

Cheers
JMS

[MDM]

Is the investment return (say 5%) assumed to be after tax ?

Usually not, because tax rates vary among types of accounts and among individuals.

Taxes are treated as expenses, the same as rent, food, clothing, etc.

[JMS]

Is the investment return (say 5%) assumed to be after tax ?

Usually not, because tax rates vary among types of accounts and among individuals.

Taxes are treated as expenses, the same as rent, food, clothing, etc.

Okay thanks.  Dammit more years!

[habanero]

Okay thanks.  Dammit more years!

I think taxes are the most under-discussed risk for a plan lasting decades. A lot of things can happen in the next 10-20-40 years and seemingly minor changes to the tax code can have big implications for the FIRE number.  Taxes are not static and they can change in ways that are good for you or bad for you. The upside is kind of irrelevant as it comes on top of an already solid plan but the downside is more of a concern. I live in a conuntry with wealth tax, so the 4% rule is more like the 3.3% rule. The idea of a wealth tax might seem remote to most americans, but who knows what will happen in 10 or 20 years? That markets might behave like they have done before, but here is no guarantee the tax regime will stay the same. 

[maizefolk]

Okay thanks.  Dammit more years!

I think taxes are the most under-discussed risk for a plan lasting decades. A lot of things can happen in the next 10-20-40 years and seemingly minor changes to the tax code can have big implications for the FIRE number.  Taxes are not static and they can change in ways that are good for you or bad for you. The upside is kind of irrelevant as it comes on top of an already solid plan but the downside is more of a concern. I live in a conuntry with wealth tax, so the 4% rule is more like the 3.3% rule. The idea of a wealth tax might seem remote to most americans, but who knows what will happen in 10 or 20 years? That markets might behave like they have done before, but here is no guarantee the tax regime will stay the same.

This is a good point.

In the USA most taxes and government benefits are apportioned based on income which makes FIRE a lot easier since our low incomes qualify us for low tax rates and potentially government benefits like subsidized health insurance.

A simple switch to looking at wealth rather than (or in addition to) income in determining ACA (healthcare) subsidy eligibility would create a big problem for many FIREee's budgets.

While we don't currently have a wealth tax, Warren is proposing is proposing 6% wealth tax on billionaires (well really a 2% tax, another 1% tax, and a third 3% tax), and Sanders a 1-8% graduated wealth tax on people with $16.5M or more in assets.

OTOH, there's a limit to what parts of the future a person can control and nothing to be gained by worrying about the parts of it outside that scope.

[JMS]

The other thing I知 interested in is how achievable is earning a 5% return on low fee index funds over say a 45 year horizon?

  I知 35 years old currently and based on our plan we will be FI by my 40th birthday.  I知 not sure whether that will be when I retire because a few extra years would do wonders for the stash.  However,  if I finished at 40 I壇 be banking on at least another 40 years hopefully.

[norajean]

A lot depends on the performance of your investments.  However, a market downturn for say a decade could result in no appreciation at all (the worst ten year period to date was actually negative return), so a conservative case might be to assume no market return for a 10 or 15 year period.

If you need $45k x 25 = $1.125 million.

If you have nothing saved today and want to be guaranteed of getting there in ten years, saving $112,500/yr would guarantee you get there.  If your investments have better than 0% return, it will happen sooner. How much sooner depends on your investment performance. You can estimate returns but there are no guarantees.

[JMS]

A lot depends on the performance of your investments.  However, a market downturn for say a decade could result in no appreciation at all (the worst ten year period to date was actually negative return), so a conservative case might be to assume no market return for a 10 or 15 year period.

If you need $45k x 25 = $1.125 million.

If you have nothing saved today and want to be guaranteed of getting there in ten years, saving $112,500/yr would guarantee you get there.  If your investments have better than 0% return, it will happen sooner. How much sooner depends on your investment performance. You can estimate returns but there are no guarantees.

I知 less worried about the returns over say the next 5 years - until we are FI in 2024.  I知 more worried about say negative returns say for 10-15 years from 2024 and the stash getting eroded away.  It seems to me that the 25x expenses might be a bit crude??

[daverobev]

A lot depends on the performance of your investments.  However, a market downturn for say a decade could result in no appreciation at all (the worst ten year period to date was actually negative return), so a conservative case might be to assume no market return for a 10 or 15 year period.

If you need $45k x 25 = $1.125 million.

If you have nothing saved today and want to be guaranteed of getting there in ten years, saving $112,500/yr would guarantee you get there.  If your investments have better than 0% return, it will happen sooner. How much sooner depends on your investment performance. You can estimate returns but there are no guarantees.

I知 less worried about the returns over say the next 5 years - until we are FI in 2024.  I知 more worried about say negative returns say for 10-15 years from 2024 and the stash getting eroded away.  It seems to me that the 25x expenses might be a bit crude??

It's all you need to know, though - "studies have been done" with all possible start points, and even if you retire at the peak of a bubble right before a crash and adjust nothing - that's the point, you still take 4% of your initial amount plus inflation every year - you're still fine.

Most of the time 4% is cautious and you'll end up with more money than your started with when you die.

If you can cut a bit of spending in the bad years, if you have a cash buffer, if you have any government pension coming... you're fine. 4% SWR is just that - safe. The most dangerous thing to the plan is you yourself.