I don't know about a cat but a 42 yacht in Turkey (1hr drive from marmaris) was £1250 per annum. That went up to £2400 if you want lift out store for 4 months. Very good value!!!
Marti Marina in Orhaniye in the Gulf of Hisaronu, Turkey has a web site here with a mooring price list. They charge based on length x width so you can work out what it may cost you. Its a lovely spot in the middle of a great cruising area and in easy reach of Marmaris, Bodrum and other cruising areas.