If the amount paid is always the same:
We've received your 10 payments of ($amount) for a total of $15,000, but you only needed to pay $12,000.
If the amount is different each time:
We've received your 10 payments which come to a combined total $15,000, but you only needed to pay $12,000.
The second sentence is fine.
The third sentence should be more like this:
We will reduce your following invoices by the amount overpaid.