Determining total w/ transaction fees

I ran into this problem the other day and have been trying to think of what equation you could use to fix this.

Credit card processing companies charge a transaction fee to the total amount processed (e.g. 3%)

If a company was owed X (e.g. $100) by a customer, how could they calculate the total amount necessary to charge so that the total minus the transaction fee would equal exactly $100?

My first thought was 100 + (100 * 0.03) = $103, but then you end up with $99.91. I realized the problem is recursive - i.e. the transaction fee will apply to itself - and I'm not sure how to go about determining that.

Thanks in advance :)