A liter of the least expensive Tortuga Rum (made in Jamaica BTW, not Cayman) will set you back around $35 US. You can usually find a bottle of the better Barcardi products like the 8 Year Old (great mixer) for $28, or many times 2 for $36 or $44 at the Duty Free stores at US airports.

You can check local Cayman prices here at Jacques Scott Liquors (a major island liquor store) and the see if there are any better deals at the Duty Free store in your airport when passing through.

Please be aware, the prices quoted on the Jacques Scott Website are in CI$ and you need to add 25% (divide by .8) to convert to USD.