| Re: Math Formula Question - Need Ideas [message #184517 is a reply to message #184514] |
Sun, 05 January 2014 00:54   |
Denis McMahon
Messages: 634
Registered: September 2010
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Senior Member |
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On Sun, 05 Jan 2014 00:26:08 +0000, Adrienne Boswell wrote:
> I have a math question to which I can't find the answer. Here is the
> scenario:
>
> Someone goes to a store and has $100.00 worth of items. The merchant
> gives the customer a 10% discount, so only $90.00 is sent to the bank.
> Of the original amount, $10.00 goes to the customer for the discount,
> $80.00 goes to the merchant, $10.00 goes for a processing fee. But
> those amounts have to be calced on the original amount, not what the
> bank got. I need a formula to find the original amount if I have the
> percentage (10%) and the amount the bank got ($90.00). I know in my
> head that the original amount is $100.00, but I have to do it
> programatically.
>
> I know this is probably dead simple, but I just can't get my head around
> it.
>
> Thanks in advance.
If a * b = c then
a = c / b
b = c / a
In your case, 100 * 0.9 = 90
Therefore to get the original,
90 / 0.9 = 100
0.9 being the decimal fraction that equates to 90%, ie the amount the
customer paid after discount.
Observation though, processing fees are usually a % of the amount paid.
eg if a card payment processing service charges 1.25%, that would be
1.25% of the payments made, so in your case:
Invoice: = 100.00
Discount: 10% = 10.00
Amount due: = 90.00
========================
Processing: 10% = 9.00
Amount to bank: = 81.00
The payment processing is only concerned with the amount of the
transaction that it actually processes, not some other intermediate
calculation between the merchant and the customer.
Consider the case where the customer is given a 95% discount by the
store. If your processing service still charges 10% of the original
amount, the your processing fee is more than actual transaction value:
Invoice: = 100.00
Discount: 10% = 95.00
Amount due: = 5.00
==================================
Processing: 10% of 100.00 = 10.00
Amount to bank: = -5.00 ???? Error
The correct math for this case is more likely:
Invoice: = 100.00
Discount: 10% = 95.00
Amount due: = 5.00
========================
Processing: 10% = 0.50
Amount to bank: = 4.50
As a general rule, payment processing systems only concern themselves
with the amounts that they are handling, and not other amounts that may
have appeared in calculations made outside of their own systems.
Of course, if you're working on something like a sales commission basis,
that might be a different set of rules, as you might expect to be
receiving a commission based on the listed price, regardless of whether
the items are sold at a discount or not.
--
Denis McMahon, denismfmcmahon(at)gmail(dot)com
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