Tax difference on dollar amounts?

Question

Why is it that on all my calculators, when I subtract 12% from $56$, I get $49.28$, but when I add 12% to $50$, I get $56$?

$56-0.12\cdot 56=49.28$ and $50+0.12\cdot 50=56$. – user26486 Jun 07 '15 at 01:01 — user26486, Jun 07 '15 at 01:01

score 2 · Accepted Answer · answered Jun 07 '15 at 01:03

2

The difference is in what exactly you are calculating 12% of.

In the first case, you found 12% of 56 which is 6.72.

In the second case, you found 12% of 50 which is 6.

answered Jun 07 '15 at 01:03

OnceUponACrinoid

772

So the problem is that the percent is increasing the amount I'm getting? The confusion arises out of the desire to reverse the percent to get back to $56 before tax. – David Metcalfe Jun 07 '15 at 01:35
I'm not sure how this relates to taxes. What do you mean by "getting"? What exactly are you trying to calculate? – OnceUponACrinoid Jun 07 '15 at 01:37

score 1 · Answer 2 · answered Jun 07 '15 at 01:01

1

Because $12\%$ of $50$ is $\frac{12}{100}\cdot 50=6$, whereas $12\%$ of $56$ is $\frac{12}{100}\cdot 56=6.72$.

answered Jun 07 '15 at 01:01

Zev Chonoles

132,937

score 1 · Answer 3 · edited Apr 13 '17 at 12:21

This is easier to understand with a more extreme example. Suppose you are earning \$100/hour and get a 50% raise. Then you're earning \$150/hour. If that's followed by a 50% pay cut you're only making \$75/hour.

It's just as bad if the pay cut comes first (down to \$50/hour) followed by the pay raise (up to \$75/hour, but not all the way to \$100/hour).

The best way to do these percentage problems is by multiplying rather than adding and subtracting. In your case 12% off means "multiply by 0.88" since there's 88% remaining. Then a 12% increase means "multiply by 1.12". Overall, your change is 0.88 * 1.12 = 0.9856, which is less than 1.

Edit: I seem to have answered this question once before, at Finding total after percentage has been used?. I like that answer better than this one.

Tax difference on dollar amounts?

3 Answers3