3 things. There has been games that used player ran banks built on trust, They've been successful for a time. Then the dude will fuck off with other peoples stuff.
Well, that's how it usually goes, I'll still offer a store house for my community to use and pay for slots which they will have their own keys. But seriously, will they really put anything of "true" value in there?
I will also have a pawn shop. So, lending would be done through that method. (and no other method.) Otherwise, the pawnshop will be an auction site and general store. (If people don't actually pawn things) You doing something with interest on top? Eh, that's not very smart people would just be "pawning" for selling. (There has to be something more worth while to hold of value?) Land, and well what else is limited in quantity to a degree that would warrant a Pawn, rather than a place to sell things. So loans with high collateral, will make sense. But be prepared for people to NOT use the service and rather just sell things. 5% interest, doesn't make sense on top of it.
Good luck having your notes, worth anything outside the locality, Sure their gold backed but only as good as anyone that can counterfeit the document you've created. If exceptionally inexperienced in the form of loaning, and using promissory notes, that could lead to inflation, that could be disastrous for your domains economy. Keep in mind even if used locally you could effectively have 1 gold held by 2 or more people at one time. This only works for as long as you can recoup and people aren't constantly withdrawing. Games in general, people actually make returns pretty frequently. Can you have them allow you to hold their money or do they think they're going to be better at it? Well it's an option if you choose to do fractional reserve banking. But still it isn't worth the risk.
Generally speaking, lending only makes sense if the economy actually evolved to require that type of thing. Yes small loans here and there. are going to be vital in some important things. Most people will not partake in that service. Because for the most part we have such an exaggerated value for homes and other things in the real world because of inflated costs. Then need to loan out to be able to afford a thing, which is either 2-4 times your annual income. Or if lucky 1/3 of your income. Most people don't save for that long and rather defer the wait. In games people generally save to gain their next prize.
People are going to be more willing to use a noble's store house than a gentry hell even an aristocrat. They have something important they can loose and they need to be kinda near that domain at all times so they can be held accountable for breaking contract to an extent that the whole government isn't in on the potential fraud that a banking system can do.