Okay, I kid. Ed McMahon was a professional and an iconic figure. Though he can no longer keep his feet on the ground, at least we can say he has successfully reached for the stars.

Moment of silence for Ed McMahon.

There’s a problem with billing the client for the fee, though: PayPal applies a fee the total, which includes the fee for which you need to be reimbursed. For example: You have an invoice for $1,000. The PayPal transaction fee is 2.9% plus $0.30, or $29.30 for our $1,000 invoice. So your client pays you $1,029.30 through PayPal. Problem is:

$1,029.30 + 2.9% + $0.30 = $30.15
$1,029.30 – $30.15 = $999.15

Sure, in the grand scheme of things, losing 85 cents on the deal isn’t the end of the world. But it got me thinking: how would I calculate the fee if I didn’t want to lose even a single penny on the deal?

Thinking back to high school algebra, I concocted this equation:

x = (x+y) – 0.029(x+y) – 0.30

In our equation, x is the amount of our invoice, and y is the fee I want to bill my client for using PayPal. In the formula, I’m applying the PayPay transaction to the total amount, not just the amount of my invoice. All I had to do was solve for y. And I won’t lie: it made my brain hurt. I like math, don’t get me wrong. I apply it to my design work all the time. And though this is a fairly simple algebraic equation, it’s not a muscle I’ve exercised in a long time. Besides, my phone is a gajillion times more powerful than my first computer; surely someone much smarter than I am has already programmed a computer to help me solve for y. Thank Google for AlgebraHelp.com. I simply entered the equation above and asked it to solve for y:

y = 0.3089598352 + 0.0298661174x

Mystery solved. From example above:

0.0298661174 * $1,000 + 0.3089598352 = $30.18
$1,000 + $30.18 = $1,030.18
$1,030.18 * 2.9% +0.30 = $30.18
$1,030.18 – $30.18 = $1,000

And I’ve saved 85 cents.

The nice thing about AlgebraHelp.com is that it showed all of the steps of the solution, which helped awaken the my dormant algebra synapse. Replacing the 2.9% in my original formula with a variable, I was able to create this final equation:

f

The client fee for using PayPal

p

The percentage PayPal charges according to your monthly PayPal income, which you can find on this chart

i

The original amount of your invoice

And here it is as an Excel formula with a corrected typo from when this was posted earlier today. I’m assuming here that A1 is your invoice amount and B1 is the percentage, so change those to your actual cell references:

=-(0.3/(B1-1))-((B1*A1)/(B1-1))

Sure, maybe 85 cents doesn’t seem like much, but on $100,000, it’s a difference of $36.11, and that could add up depending on what kind of business you operate. I don’t expect to be billing $100,000 per month—ever—but at least I know I’ve accounted for every last cent.

I’m sure someone else out there in the internets is looking for the solution to this problem, so I hope this friendly post is helpful. Of course, you should be upfront with your clients about how you are calculating this fee.