Tax or no tax -- how much difference?
You've probably never given much thought to just how much of your earning power is siphoned off by taxes. Well, as it turns out, the ability to grow your wealth without taxes is an unbelievable difference from that ability to grow it without the drain of taxes: Be prepared for a shocker.
The purpose of this page is to lay out two scenarios of doubling a single dollar for twenty-one periods: one, a pure double; the other, with the increase taxed at 30%. For those who are rigorous math people, we've put the formulas, so that you may verify this for yourself (as you may find this very hard to believe, without it.)
The Non-Taxed Doubling Example
Let's start simply with the non-taxed doubling example which is, in this case, where the TOTAL amount is doubled each period. The formula is relatively simple, below. To speak it first in English, it says ...the Original Investment x 2 (which is our "doubled", per period) then raised to the power of the number of periods (years, in our example.)
i x 2^n
Where i = Original Investment, 2 = factor of "double", N = numbers of periods
Presuming a $1 initial investment, at the beginning (n=0), formula = $1.
After year one, (n=1), amount = $2
After year two, (n=2), amount = $4
After year three (n=3), amount = $8
After year four (n-4), amount = $16
. . .
After year twenty, (n=20), amount = $1,048,576
The Taxed Doubling Example
This next example would be the same starting $1, but the original amount and its subsequent increase is taxed at some rate (say 30%) -- So, it would be the original amount, first taxed, THEN doubled. And then, each year, the NEWLY INCREASED amount is taxed before adding it to the prior. This is not double-taxing, but only taxing the "increase," before allowing you to put it into your coffers -- as is our current tax system today. The math for this is a little more complex, so I'll elaborate:
This doubling formula is along the lines of: some original amount, plus it's doubled amount after tax, or: Amount + [Amount x (1-tax rate)]
Example: In the case of a 30% tax rate, this is:
Amount + [Amount x (1-.30)] =
Amount + [Amount x .70] =
1 Amount, plus .70 more Amounts = 1.7 Amounts, or = Amount x 1.7
This process goes on for however many days, and similarly to the first example is expressed as 1.7^n.
..Or, the whole formula is (again, in English,) The Original x 1.7 raised to the number of periods, or:
i x (1.7)^n
Where i = Original Investment, in this case $0.70 after the first tax period; N = numbers of periods
Another way to look at this is that the original investment amount is not quite doubled, but it's second portion is reduced by .30 tax rate, and therefore equals, not 2, but 1.7 x the previous number:
At the beginning (n=0), beginning amount = $1.00 less 30% = $0.70
After year one, (n=1), amount = $1.19
After year two, (n=2), amount = $2.02
After year three, (n=3), amount = $3.44
After year four, (n=4), amount = $5.85
. . .
After year twenty, (n=20), amount = $28,449
Without doing a distraction, for those would like to see the general formula that works for all tax rates, this is below. I include this because surely some will think that I used an unreasonably high tax rate (30%?) to make it look dramatic. It's dramatic either way. For those who would like to plug in a different tax rate other than 30% used in the above example, here's the formula:
[i x [(1-tax rate)] x [1 + (1-tax rate)]^n
Where I = Original Investment, in this case $1; N = numbers of periods
Try it: If you plug in the original $1, and .30 tax rate, you'll see that this is the above shown $28,449 number after twenty years. (Likewise, you'll see that the first example of 0% tax rate also gives the correct amount.) As a third example, if you use $1 and a .22 tax rate, that after-twenty-year number is $79,523.
This is astounding! Absolutely speechless astounding. Taxing the substance that we would use to otherwise earn and multiply is more than just a minor deduction: It effectively entirely saps off our ability to grow wealth, relative to a non-taxed environment.
We've come to accept this as either "necessary," or "only a little bit." Some may argue that taxes are good, or necessary. It's not my purpose to debate that here. My purpose here is simply to open your eyes to the math: We've accepted a taxed portion going away as a minor or necessary evil. But did you ever comprehend that so much was actually being drawn off of your substance? I know I didn't.
Here are the numbers: $1,048,576 or $28,449. --Which would you choose?
Choose? Yes. You have that option.