There would be 2 banking system: simple, extended. In simple system there would be one account to all holds. For extended system, every hold would have 

separately account. At the start there would be npc in every jarl palace to manage accounts. 

Account types :

• normal account - you'll locate gold in account without any profit. gold can be stolen  but you can buy insurance for it for 10 gold per day
• investment account - gold in this account can increase or decrease at the start depending on random factor, later it can depends on Skyrim situation or any other mod
• debt account - in this account you can get some debet which you need  to pay up to 500 gold with more interest rate than taking small loan

Loan type:

• small loan - maximum of 1000 gold with interest rate for exact time, you need to return this in time.
• big loan - maximum of 20000 gold with interest but you have up to 30 weeks to return full of it but you need to pay rate once a week 

LIan additional function:

• you can pay it to npc or it would be taken from your account
• you can miss one rate without consequences

Consequences of not paying

• increase of next payment
• bounty 
• sending bounty hunters

Opening account

when you open account you'll get paper that you own it.

if you lose it you'll need to wait one day for new paper with fee of getting it.

with extended system there would be possiblity to send gold from hold to hold. with a risk of something happening on road

also I want to add integration with slavery mods

slaves pay more and gets less, some features can be blocked.

your master can open account and you can use it with maybe more 

API

stealing gold

change of investment rate

statistics of account

you can take loan or get debt

master can take loan and you need to repay this

block possibility of having account or closing your account by master