Calculate the good Paypal fees

Question

I have a problem of ethics and mathematics...

I have a website with subscription fees. My customers can pay them with paypal.

Paypal takes 3,4% of my price + 0,25c of fixed fees.

If my customer pay 10, paypal take me 10x0,034 + 0,25 = 0,59 ... I earn 10-0,59... So I want to include before the paypal fees because i want "+10" in my account and not 9.xxx or 10.xxxx

I ask to my customer to pay 10+0,59 = 10,59 ... but this time Paypal fees are 10,59 x 0,034 + 0,25 = 0,61 and I earn 10.59 - 0,61 = T____T

So... I decide to increase the percentage. 10x0,035 + 0,25 = 0,60 ! And paypal calculates 10,60 * 0,034 + 0,25 = 0,61... T____T

So... Up the percentage to 3,6% ... 10x0,036 + 0,25 = 10.61 ! And paypal... 10,61 * 0,034 + 0,25 = 0,61 ! 10,61 - 0,61 = YES !!!!

My question is... Is there a way to calculate a correct percentage to be applied before paypal fees?

Answer 1

In principle you have to solve for $x$ the following equation,

$$(1-0.034)x - 0.25 = 10$$

$x \approx 10.61077$ and it gives you the amount needed to obtain \$$10$ after fees.