Credit card processor charges, for each transaction, $2.9\% + \$0.30$.

I need to find an amount that covers that cost, from $\$5$ to $\$5,000$, on a per item basis, all while maintaining a small profit.

For example, a customer may want to purchase 3 items. Each item has a different price and possibly a different fee structure based on whether or not it's a for-profit purchase or non-profit purchase.

Item 1 is $\$10$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.

Item 2 is $\$80$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.

Item 3 is $\$25$ and non-profit so we need to account for the processing fee only- no profit.

What I cannot determine is a full-proof way to account for the fees all the way up to $5,000 without losing money on the processing fees.

  • $\begingroup$ You have used the dollar sign. It has confused the mathjax interpreter. Please use something else like £. $\endgroup$ – Ali Caglayan Aug 19 '13 at 14:34
  • $\begingroup$ @jasonsfa98: Welcome to MSE! There is still a problem with the dollar signs. Also, do you have thought on the problem and can share what you have tried as it helps responders? Regards $\endgroup$ – Amzoti Aug 19 '13 at 14:49
  • $\begingroup$ I've set things inside MathJax with backslashes in front of the dollar signs and percent signs that are supposed to actually appear. The same thing works in standard LaTeX. $\endgroup$ – Michael Hardy Aug 19 '13 at 17:43

I will ignore dollar signs. Suppose that $C$ is the cost of the product and we wish to charge $C + X$ for the product. The processing fee is $.029(C + X) + .3$. We need to solve $$(C + X) - (.029(C + X) + .3) \geq C$$ for $X$. In this equation $C + X$ is what we charge and $.029(C + X) + .3$ is the processing fee. If the difference is greater than $C$ we make a profit. There are probably other costs that are not mentioned in this problem. Presumably they are included in the value of $C$. In any event we need $$.971 X \geq .029 C + .3.$$ We can solve for $X$ as follows: $$X \geq \frac{.029 C + .3}{.971}.$$ There is no upper bound for the value of $X$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.