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You can pay by cash, but be prepared to join a long queue at the purser's desk on the morning of disembarkation. We have a credit card purely for use on cruises and we settle the full amount on our return so as not to incur any interest charges. If you do use a credit card, make sure that you do not let the cruise line do the currency conversion for you, leave it to the credit card company. Full details of methods of payment should be found in the 'Cruise Answer' booklet you receive about 10 weeks prior to departure. Enjoy your cruise.
If I could offer another good reason for having a credit card it could get you out of all sorts of trouble when travelling abroad. Who knows they are not going to have an accident, need medical treatment, fly to the next port because you were late back to the ship, need to fly home at short notice. Unless your walking around with a pocketfull of local currency , which is never a good idea in some of the ports, your credit card is a great security backup should things go wrong. Sorry to be 'doom & gloom', but I wouldn't step ashore without one!