I purchased a large value item from a chain store and have been undercharged - what is my position legally?

When the sale istant processed the credit card transaction, they entered a lower figure. I noticed the difference and asked to her check the amount and goods were correct. She responded "yes". 10 hours later, the shop rang me and gave me 24 hours to pay the difference or they would refer the "debt" to a collection agency. I know I good a good deal, but I did give her an opportunity to correct the error. Where do I stand legally? Is the debt payable? Should I battle this one? New Zealand Law please.