In a reopen, the coupon rate of a note or bond is the same as the original issue. So you know the coupon. The price will fluctuate to give you the ultimate market rate. Hence, you can very well pay a premium for a reopen, i.e. you might pay $101.55 for a note, for example. Or, the price could be at a massive discount.
I want to point out that paying a premium on a Treasury Note or Bond creates a new tax task that someone may not have encountered before if all they have done in the past is buy at auction, which almost always has a small discount on the Note on original issues. It is usually pretty straight forward, but can get complicated if the numbers are large.