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Shockingly Simple Math

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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’d 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’d need To contribute X in order to retire in 10 years, or maybe we’d 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

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