I mean, technically no they don't. But that's just being pedantic. They charge the bank based on gross dollar volume, and the bank gets the money to pay for that from... interchange fees. The more volume the bank does, the more they pay and the more they get from interchange fees.
Interchange fee pricing is set based on how much mastercard charges the banks, so while technically true, the interchange fees are basically set by mastercard's pricing.
Interchange fee pricing is set based on how much mastercard charges the banks, so while technically true, the interchange fees are basically set by mastercard's pricing.