Need Cell To Display Set Minimum Number

I'm trying to analyze the pricing we get from our shipping courier. Although the courier gives us incentive discounts, they also have a minimum charge that supersedes the discount. In other words, suppose the "Minimum charge" is set at $6.24. If the published "list rate" on a package is $10 but we get a 50% discount on all shipments, instead of paying $5, we pay $6.24. Basically, between the post-discount amount and the "minimum charge" we pay whichever is greater/higher.

Now, to the Excel part: I have cells with simple formulas applying our % discount to our carrier's published list rates to calculate the resulting price (i.e, where cell A1 contains published list shipping rate and cell B1 is our discount %, so in cell C1, I have a formula: =A1*B1). I would like know how, if the result of the formula in cell C1 is less than $6.24, that the cell could display $6.24 rather than the actual result?