In medieval times, there did exist moneylenders who would perform many of the same functions as today's banks. AFAIC the two main differences are accessibility and security. (A moneylender is just one guy, not a corporation with branch offices; if you want your cash, you must travel to him and get it. And he's not FDIC-insured, so if his office gets robbed and your money gets stolen, you're out of luck.)
If your gameworld doesn't have moneylenders (or your DM doesn't feel like dealing with them), buy stuff. Invest everything you can in weapons, armor, potions, and other adventuring gear. Eleven thousand gold pieces is just a big pile of metal; a Wand of Dispel Magic is easier to carry and may save your life.