make sure we're charging fees properly

[chadwhitacre]

Raised by @rcross on #1664:

So it seems that there was a decision made to change the fee computation function, though there doesn't seem to be a rationalisation for why it was changed. In my opinion, the new function is actually incorrect based on the stated fees.

I would expect (X * 1.029) + .30.

However, even if it is (X + .30) * 1.029 this is not the same as (x + .30) / .0971

It is usually a negligible difference that is rounded out, but on large amounts it does make a difference.

For $100:

100_1.029 + .30 = 103.20
(100 + .30)_1.029 = 103.21 (103.2087)
(100 + .30) / .0971 = 103.30 (103.29557158)

for $5000 = [5145.30, 5145.31, 5149.64]

Is this rounding error intentional?

Related issues: #1031

[chadwhitacre]

@rcross Good catch! It's not a rounding error; it's intentional. We should update the About/FAQ pages.

When we launched we were charging an additional $0.30 + 3.9% on credit card transactions, using most of that to cover Balanced's card processing fees, and the rest to cover hosting, etc. The fee computation was actually 100 - ((100 + 0.30) * 1.039) = 4.22 (rounded up), and the About page reflected this (fees weren't mentioned on the FAQ at the time):

We add an additional 30¢ + 3.9% fee when pulling money in from your credit card, to cover credit card processing (as well as hosting and other expenses).

One of our open company principles is to charge as little as possible, so in #1031 we dropped our card processing fee to cost, with the rest of Gittip's funding coming from tips to the Gittip team account on Gittip. The fee computation since 20b5fa0 has been ((100 + 0.30) / (1 - 0.029)) - 100 = 3.30 (rounded up). The reason is that Balanced computes their fee as 0.029N - 0.30, and we want you to end up with 100 in your Gittip balance, so we compute the fee using the inverse of Balanced's fee function.

From the point of view of the amount we actually charge you, $103.30, the fee is indeed (N * 2.9%) + $0.30. However, from the point of view of the amount you are trying to give on Gittip, $100, the fee is (N + 0.30) / 0.971.

[chadwhitacre]

See #2160 for modified language:

We upcharge to cover a processing fee of 2.9% + 30¢ when pulling money in from your credit card.

[rcross]

Thanks for clarifying - sounds like someone should tell Balanced that they aren't calculating their fees correctly then.

fwiw - I still think this is wrong. X - ((X + 0.30) / (1 - 0.029)) = gives you a negative value. I think it should be $fee = Y - (Y -.30)/(1+.029)

Balanced's function (if its as you stated) equally gives an incorrect value, as that would be the value without fees.
This makes the fees equivalent to X_(1/.971) + .30 == X_1.0299 + .30, which suggests we need to say 2.99% (or 3% if rounding) + 30¢
Maybe I'm just being pedantic, but it makes a difference when you start looking at larger sums and it doesn't seem to be inline with how other gateways calculate their fees.

Here is the algebra for my $fee equation:

Where X = the base transaction amount, and Y = the total amount charged,
$fee = X*.029 + .30 
Y = X + $fee
Y = X + X*.029 + .30 
Y = X*(1+.029) + .30
X = (Y -.30)/(1+.029)
$fee = Y - X
$fee = Y - (Y -.30)/(1+.029)

[chadwhitacre]

X - ((X + 0.30) / (1 - 0.029)) = gives you a negative value.

Sorry, I misspoke. Corrected above from:

100 - ((100 + 0.30) / (1 - 0.029)) = 3.30

to:

((100 + 0.30) / (1 - 0.029)) - 100 = 3.30

[chadwhitacre]

Balanced's function (if its as you stated)

Another error on my part, sorry for being so sloppy here. I've corrected:

N - 0.029N - 0.30

to:

0.029N + 0.30

[chadwhitacre]

2.99%

Where is this coming from? Did I introduce 2.99% at some point (rather than 2.9%)?

[rcross]

1/.971 = 1.029866.... i.e. 2.99%

this is ultimately the crux of the issue. Dividing by (1-%fee) is not the same a multiplying by the actual %fee.

[chadwhitacre]

Here is the algebra for my $fee equation:

I believe this is the crucial error:

$fee = X*.029 + .30

Isn't $fee calculated on Y, not X? We have X (the amount you want to give) and a function for $fee in terms of Y. We need to solve for Y.

[chadwhitacre]

Here is the problem:

Where X = the target amount by which you want to increment your Gittip balance, and 
      Y = the total amount we are going to charge you in order to hit your target,
$fee = Y*.029 + .30
Y = X + $fee

What is the function for X in terms of Y?

[rcross]

I'm pretty sure the $fee is calculated based on the amount you want to give. However, my algebra also solves for Y.

In english:
If I want to give $100, then I need to pay $100 * 1.029 + .30 = $103.20 of which $3.20 will go to Balanced

If I want to be charged $100, then I will have ($100 - .30)/(1.029) = $96.89 added to my gittip balance, and a fee of $3.11 will go to Balanced

[rcross]

as above,

in terms of Y
$fee = Y - (Y -.30)/(1+.029)
X = (Y -.30)/(1+.029)

[chadwhitacre]

I'm pretty sure the $fee is calculated based on the amount you want to give.

No, it is not. Balanced computes their fee based on the amount we tell them to charge you.

If we tell them to charge you $100.00, they are going to charge you $100.00, and extract a fee from us of $3.20, and we will credit your Gittip account $96.80.

If we tell them to charge you $103.30, they are going to charge you $103.30, and extract a fee from us of $3.30, and we will credit your Gittip account $100.00.

However, my algebra also solves for Y.

Your algebra begins with a faulty assumption:

$fee = X*.029 + .30

should be:

$fee = Y*.029 + .30

[chadwhitacre]

No, it is not.

I should say, that's not how Balanced calculates their fee (per example directly above). We on the other hand need to compute Balanced's based on the amount you want to give. Our fee function needs to be the inverse of Balanced's.

[chadwhitacre]

IRC Q.E.D. :-)

[rcross]

After discussion in IRC, chad is correct on the fact that the fee is calculated based on the amount charge and then deducted.

So, in that case

Where X = the target amount by which you want to increment your Gittip balance, and 
      Y = the total amount we are going to charge you in order to hit your target (and the amount used for calculating fees)

$fee = Y*.029+.30
Y = X + $fee
X = Y - $fee
X = Y -  (Y*.029+.30)
X = Y - Y*.029 - .30
X = Y(1-.029)-.30
Y = (X+.30)/1 - .029) 

So, in english:
If I want to give $100, then I need to pay ($100+ .30)/(1-.029) = $103.2955 ($103.30 rounded) of which $3.30 will go to Balanced

If I want to be charged $100, then I will have $100(1 - .029) - .30 = $96.80 added to my gittip balance, and a fee of $3.20 will go to Balanced

Which makes the current approach correct. Apologies for the effort required to clarify this. It also appears that contrary to my assumption (perhaps I was channeling paypal??) that most other gateways calculate it this way as well, so the change to wording is probably sufficient.

[chadwhitacre]

Apologies for the effort required to clarify this.

No apologies necessary! I'm grateful to you for taking the time to hash this out. This is a crucial aspect of Gittip and we need to make sure it is correct. Having this discussion in public means that the next person who has the same question can simply review the ground we've covered here. :-)

Cheers! 🍻

[chadwhitacre]

P.S. If you want to dive into PayPal, check out masspay.py (which has pending updates in #2097 #2098 #2099). ;-)

[chadwhitacre]

You might also have fun with #449 and steady_state.py (which we're not actually using yet).