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Let's say a credit card processor wants to charge $(3\% + \text{US}\$ 2)$ for all transaction. What formula do I use to make sure that after the charges are deducted, I get the figure I want.

Example: If my product is $\text{US}\$ 100$ How much do I need to increase the price so that I will get $\text{US} \$100$ even after the transaction is charges by the credit card processor.

If it is purely $\% $-based, then I believe it is $\dfrac{\text{US}\$100}{1-0.03}$. But with the $\text{US}\$2$ in play, I am not sure how to do it. Please help :)

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up vote 4 down vote accepted

Let $x$ be the price we charge. Then there is a transaction fee of $3$ percent, that is $0.03x$. There is an additional charge of $2$ dollars.

So we end up with a net amount of $x-0.03x-2$. We want this to be (say) $100$.

Thus $$x-0.03x-2=100.$$ Simplify this first to $x-0.03x=102$, then to $0.97x=102$. We find that $$x=\dfrac{102}{0.97}.$$

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That's it. Thank you for your prompt respond :) – Lasker Jan 29 '13 at 7:43
You are welcome. I am sure it is clear to you what to do with a target amount different from $100$, and what to do when the fees go up. – André Nicolas Jan 29 '13 at 7:48
Yeah, that is clear. Thanks :) – Lasker Jan 29 '13 at 7:50

$100=(1-\frac{p}{100})x-2$ so $$x=\frac{102}{1-\frac{p}{100}}$$

To account for the $2$ dollar surcharge, you can think of the price of the item as being $102$ with surcharge, then apply what you have already figured out.

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Thanks for your answer :) – Lasker Jan 29 '13 at 7:50

Okay just for my understanding, for \$100, they will charge you 3% (=\$3) + \$2 so you are finally left with \$95? If that is the case I understood your question correct.

Let us assume you are at an ATM and click the "\$X" option. What you get is not \$X, but $\$X \cdot(100\%-3\%)-\$2$ so you are left with $\$X\cdot0.97-\$2 $. If you actually want to have \$100 after they charged you, you want $\$X\cdot0.97-\$2 $ to equal \$100.

So you have to solve $\$X\cdot0.97-\$2 = \$100 $ for $\$X$. The results in $$ \$X = \$102/0.97\approx \$105.15 $$

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Thanks for your answer :) – Lasker Jan 29 '13 at 7:51

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