5 votes

Tax Increase Deception (14.7% equals 5%)

Has anybody else noticed that when someone talks about a 5% tax rate increase (on, hypothetically, a current rate of 34%), they neglect to mention that that is effectively an increase of 14.7%? [edit: i.e. you will pay 14.7% more in total taxes than the previous year]

For example: (using http://www.calculatorsoup.com/calculators/algebra/percentage...)

Calculate percentage change
from V1 = 34 to V2 = 39

[ ((V2 - V1) / |V1|) * 100 ]

= ((39 - 34) / |34|) * 100
= (5 / 34) * 100
= 0.147059 * 100
= 14.7059% change

= 14.7059% increase
Calculate percentage change
from V1 = 15 to V2 = 20

[ ((V2 - V1) / |V1|) * 100 ]

= ((20 - 15) / |15|) * 100
= (5 / 15) * 100
= 0.333333 * 100
= 33.3333% change

= 33.3333% increase

For example, here's the percent increases of other rate increases:

10% to 15% = +50%
25% to 28% = +12%
28% to 31% = +10.7%
33% to 36% = +9.1%
35% to 39% = +11.4%

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When Calif. was voting on the largest tax increase

by any state in U.S. history a few years back, I tried to explain the same thing to my six fellow board members at a meeting. None of them except one guy "got it". The tax increase was approved but repealed later only to be approved again this year.

semantics wrong

as a mathematician, i know that misunderstanding basic logic and mathematical first principles is what is wrong with society as a whole.

assume the following:

n is the current tax rate.

now, let i = increase of tax owed (not increase in tax rate).

in your example, we let n = 34 / 100 = 34 % and i = 5 / 100 = 5%.

now, suppose i make $100,000 this year of taxable income, assuming that there is such a thing as taxable income. this comment is not a comment on whether or not that that taxable income exists. for the purpose of this exercise, we assume it does.

now, using the current rate of n, we can calculate the amount of tax owed. this is n * $100,000 = .34 * $100,000 = $34,000.

next, if we have an increase of the amount of tax owed by 5% (and not an increase in the rate) an increase of i of $34,000 is going to be (1 + i)*$34,000 = (1 + .05)*$34,000 = 1.05*34,000 = 35700. o, we see that the increase is $1700.

by the magic of algebra, $1700 / $34000 = .05 = i.

now, assuming that an argument of semantics is necessary, and the government officials pass a law for the increase of the tax rate by some fixed amount i, then we get the following scenario.

if we want to increase the tax rate by i, then, the new tax owed would be (i + n) * $100,000 = $39,000.

now, the difference in the new tax owed with the increase versus the old tax owed is $39,000 - $34,000 = $5,000.

surprisingly enough, $5,000 / $35,000 = 1 / 7 = 14.705...%.

so, we see that there is both a semantic difference as well as a logical difference between an increase in the tax rate or an increase in the amount of taxes owed.

i say we look at all the bills that call for an increase in taxes, and show the people the math as to how this works! if the language in the law calls for an increase in the tax owed, then our representatives have, perhaps unknowingly as the average american is so inept at basic algebra, lied to us. we must also compare the language used on the campaign trail and compare to the actual wording that is in the law.

i offer this math lesson to you, pro bono. fortunately, i can write this expense off, as this has taken me approximately 1 hour of my time to elucidate the math, as well as other base logic, to you and the rest of the DP. For other mathematical inquiries, questions, or consultation, I am Mathemagic Solutions, LLC. Feel free to visit my website: www.mathemagicsolutions.com for any other questions, comments, or concerns regarding mathematics, business, consulting, or solutions.

"Surprisingly enough, $5,000 / $35,000 = 1 / 7 = 14.705...%."

Where did the $35,000 come from? If they say 5% increase is it actually more than 5% in real money(in terms of this exercise of course).?
I am kinda confused about what you guys are talking about. Please help me understand better.

Typo, should be $34,000

Basically, the confusion is that even though your tax rate goes up 5%, depending on the starting rate, you will pay a higher percent change in tax dollars (i.e. if you pay $1,000 one year, then $1,200 the next because of a rate increase, the percent change is 20%).

I'm not sure what the meaning of this is, though. I think it may indicate the rate of revenue increase to the gov't...


... for noticing the typo. even i am not immune to mathematical errors. but i hope i effectively got the point across.

I agree with your analysis

You're right, I should have been more clear with the terms. After reading your post, I think I also see it from another angle.

I've noticed that it's common for articles to say that "If you make more than $50,000 your taxes will go up by $1,000" (i.e. reader sees a 2% increase), but what they neglect to mention is that the percent change could be an 8.7% increase in revenue to the IRS! (Assuming, say changing from 23% to 25%).