The words that immediately come to mind are "surcharge" and "fee". Consider the following:
Basic cable service provides 50 standard channels for a set price of $30 a month. As for the premium channels, you may order them for an additional surcharge of $20.
...or the following:
Standard repair service rate for a computer is $40 an hour. There is, however, an overnight fee of $10 for every night the computer is kept in our possession, after the repair is completed. We notify you after we have completed the service, and for every day that passes, you incur this extra fee.
I am just utilizing random numbers on the example sentences, but I hope they help clarify usage.