Lender provides a few useful banking options, that don't have a huge impact on the game, but are a welcome addition nonetheless.

Take out loan

A loan can be granted in any city with a trading office. You can receive a maximum of three loans.

Repay loan

Here you can repay your debts. Any loans you took out, as well as official fines and taxes for completing a Town Wall are dealt with in this tab.

Grant loan

Addendum on Granting Loans
I gave out loans to various lendees for 3 years so far and recorded each loan. As the paragraph above says, the rate of return is better on trading goods than on loans.

There are different types of lendees though. If you grant loans to everyone, from traders, travelling merchants to Patricians, your rate of return will be near 0% or even negative because of the default rate. If the lendee defaults, you lost your money. I won't count the goods or ships you get because some of the time, the game advises you to release the lendee from the debt to help your reputation.

However, if you lend only to Councillors, Patricians or Lord Mayors, your rate of return will be around 19%. There will still be defaults but the repayment rate is 93% (that is, these types of lendees will repay their loans 93% of the time and default on their loans 7% of the time).

19% isn't bad but you can make more if you invest in workshops and trade goods. Granting loans for profit should only be done if you have excess cash that can't be used for anything else.

If you have enough gold, you might want to consider lending some of it to your fellow traders. You need to have a trading office in a town to do it. There is no limit to the number of loans you can grant, but requests for new loans appear only once in a few days.

The profit from this is rather low even with high interest rates (compared to trading).

Granting loans can be used as a long-term bank investment of sorts, if you have some excess gold that you won't be able to invest otherwise for a few months. When you have offices in multiple cities (8 or more preferrably), grant all available loans every few days. After a few months you will be receiving gold almost every day (or even multiple times a day). These are minor profits that do add up over time.

There is a possibility that a trader will not be able to repay a loan. In that case you will be given an opportunity to release his debt or to impound some of his property. This choice will have some impact on your reputation. The goods you will receive will depend on the amount of gold the trader owes you. You can receive a few loads of goods for small debts, a snaikka with a few goods for medium debts, or a crayer for debts in the 30000 range. This is a decent way to acquire new ships at a lower cost.

Granted loans

This is a list of all the loans you have granted.

Buy shares

This option is useful only in Multiplayer. You can purchase shares of other players' companies, and receive a percentage of their profits.

In Single Game you can only buy back the shares of your own company, if you have sold some earlier. The shares will only be offered if your company is losing value (if you start losing profit, or if your Company Value goes down).

This can be exploited if most of your Company Value is in cash, but it becomes more difficult if you have a lot of investment in buildings.

Sell shares

This option allows you to sell a part of your company to other players. It can be useful in Multiplayer, while it's nearly useless in Single Game mode.

If your business is doing well, you will see an offer to purchase a percentage of your company's shares, for an amount equal to that percentage of your Company Value. Then again, if your business is doing well, why would you sell your shares? It's not easy to get them back if you change your mind later, so other options should be considered if you are desperate for cash.