Figuring a formula to calculate a percentage

[SummitAutomotive]

Hello math forum,
I am new to this organization and would like to begin by thanking everyone in advance. My name is Philip and manage an automotive shop.
The overwhelming costs of credit card processing has forced us to impose the credit card interchange fee to all customers using a credit card to pay invoices.
In some cases we are waiving this fee, and need assistance with the equation/formula to properly calculate.
I will use the exact number that has us stumped to simplify things.
The invoice total is $2,952.25 . There is an automatic processing fee of 3.5% which calculates the fee to $103.33, which increases the charge total to $3,055.58
Our credit card machine allows us to enter a dollar amount discount, in which we entered the $103.33 . So here is the dilemma.
The credit card terminal applies the 3.5% to the discounted total of $2848.92 which then gives us an incorrect total of $2948.63.
Any help figuring the equation how to get to the proper invoice total by applying a discount and including the 3.5% charge, would be highly appreciated.

 

[tkhunny]

How do you enter it without any fee or discount?
How do you enter it without any discount?

 

[Dr.Peterson]

Hello math forum,
I am new to this organization and would like to begin by thanking everyone in advance. My name is Philip and manage an automotive shop.
The overwhelming costs of credit card processing has forced us to impose the credit card interchange fee to all customers using a credit card to pay invoices.
In some cases we are waiving this fee, and need assistance with the equation/formula to properly calculate.
I will use the exact number that has us stumped to simplify things.
The invoice total is $2,952.25 . There is an automatic processing fee of 3.5% which calculates the fee to $103.33, which increases the charge total to $3,055.58
Our credit card machine allows us to enter a dollar amount discount, in which we entered the $103.33 . So here is the dilemma.
The credit card terminal applies the 3.5% to the discounted total of $2848.92 which then gives us an incorrect total of $2948.63.
Any help figuring the equation how to get to the proper invoice total by applying a discount and including the 3.5% charge, would be highly appreciated.

They are effectively multiplying $2,952.25 by 1.035 to add on the fee; that gives a total of $3055.57875 (which is then rounded).

You want the total to be $2,952.25; so you need to reverse the process by dividing by 1.035: $2,952.25/1.035 = 2852.42 (rounded).

Then, when you enter this as the (discounted) amount, you will be charged 0.035*2852.42 = 99.8347 (rounded to 99.83?), bringing the total to 2952.25, as you want. That is, you should be able to enter 99.83 as the discount, and get the total you want. See if it works.

 

[SummitAutomotive]

They are effectively multiplying $2,952.25 by 1.035 to add on the fee; that gives a total of $3055.57875 (which is then rounded).

You want the total to be $2,952.25; so you need to reverse the process by dividing by 1.035: $2,952.25/1.035 = 2852.42 (rounded).

Then, when you enter this as the (discounted) amount, you will be charged 0.035*2852.42 = 99.8347 (rounded to 99.83?), bringing the total to 2952.25, as you want. That is, you should be able to enter 99.83 as the discount, and get the total you want. See if it works.

Dr. Peterson,
We could not have asked for a better explanation. It worked great. Very highly appreciated!
-Philip