1

Is there a mathematical concept involving prediction of a resulting value from a set equation?

Here is the situation. A payment processor charges 2.9% + $.30 per credit card transaction. A non-profit wants to allow donors to cover this fee. The non-profit needs to show their donor what the fee will be on their donation of x dollars.

In this situation the non-profit can't simply say the fee is = (x * .029) +.30 because the payment processor will charge the processing fee on the the total of the donation. Each time you add the fee to the donation the fee increases. I'm sure this is a know mathematical concept, I just don't know what the name for this is or how to approach solving it.

Thanks

JoshJoe
  • 113
  • The fee is going to be assessed: there is no way around that. But perhaps what you're trying to ask is: if a donor wants to make sure the non-profit receives $X$ dollars, not $X$ minus the processing fee, how much should the donor donate? Well, say the donor donates $Y$. Then you want $Y-(0.029Y+.30)=X$. Solve for $Y$. – symplectomorphic Jun 01 '15 at 04:51

1 Answers1

1

If I understand the problem correctly, you want to be able to tell the donor what her donation $d$ should be so that the non-profit will retain an amount $r$. We have $$r=d-0.029d-0.30\tag{1}$$ and want to solve for $d$. We have $r+0.30=0.971d$, and therefore $$d=\frac{r+0.30}{0.971}.$$ After the computation, one might want to do some rounding.

If you want to tell the donor what the fee will be for a net retained amount $r$, calculate $d-r$.

André Nicolas
  • 507,029
  • This is how I interpreted the problem, too, in my comment above. Though I love the sentence "Each time you add the fee the fee increases." What a lovely way to solicit money. – symplectomorphic Jun 01 '15 at 04:55
  • @symplectomorphic: Many charities use "middlemen" who absorb a far larger percentage of the donation, from $50%$ up. That information would be nice to know. The credit card transaction cost is tiny in comparison. – André Nicolas Jun 01 '15 at 05:06
  • yes, indeed. I was making a joke, or trying to anyway. (By taking the quoted sentence a little too literally.) – symplectomorphic Jun 01 '15 at 05:09
  • @AndréNicolas Thanks for your answer. The result is a little off from what I was trying to get. I modified it to this, which results in the total gift amount. Thanks 
    d=r+0.30/.971+0.30
    – JoshJoe Jun 01 '15 at 05:26
  • @AndréNicolas woops. You had it right, I just forgot my ordering should read d=(r+0.30)/.971 – JoshJoe Jun 01 '15 at 05:31
  • @symplectomorphic I got your joke and laughed : - ) – JoshJoe Jun 01 '15 at 05:33