Take out loan
You can take out a loan in any town in which you have a trading office. You can be granted a maximum of three loans. This option becomes much more useful on higher difficulty levels.
Repay loan
Here you can repay your debts, in full or in part as you choose. The total amount repayable of each loan you have taken out is listed here, together with any amounts payable from official fines and taxes for building a Town Wall.
Grant loan
There are different types of debtor though. If you grant loans to everyone, from traders to travelling merchants to Patricians, your rate of return will be near 0% or even negative because of the default rate. If the debtor defaults, you lose your money. I won't count the goods or ships you get because some of the time, the game advises you to release the debtor from the debt to help your reputation.
However, if you only lend to Councillors, Patricians and Lord Mayors, your rate of return will be around 19%. There will still be defaults but the repayment rate is 93% (that is, such borrowers 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 build 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.
Compared to trading, the profit gained from loan interest is rather low - even with high interest rates. Loans are a minor source of profit, but they do add up over time.
Granting loans can be seen as a long-term investment of sorts, if you have some excess gold that you wouldn't otherwise be able to make money from for a few months. To maximise this strategy, once you have trading offices in multiple cities (8 or more preferably), grant all available loans every few days. After a few months you will getting gold from loan repayments once, or even sdeveral times a day.
Sometimes, a trader will not be able to repay a loan. In that case you will be given the option to release his debt or impound some of his property. This choice will have consequences for your Reputation. If you choose to impound property, what you receive will depend on how much the trader owes you. You typically get a few loads of goods for small debts, a snaikka loaded with a few goods for medium debts and a crayer for debts of around 30,000 gold. This is a decent way to acquire new ships quickly, though at a slight cost to your reputation.
Granted loans
This is a list of all the loans you have granted. The date of repayment and amount outstanding are displayed.
This option is only useful in Multiplayer. You can purchase shares of other players' companies, after which you will be paid 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 (i.e. if you start losing money 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 a lot of your capital is tied up in buildings.
This option allows you to sell a part of your company to other players. It can be useful in Multiplayer, while it's all but 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 if you are desperate for cash, you should consider other options.