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Pension pot is the money, the employee and sometimes the employer and the government pay that gets accumulated into pension fund.

But my question is, that this pension fund is basically a bank account, and does this account get interest over the years?

I need to know this because I want to understand pension calculators better.

The companies have access to a big sum of money over the years and they pay it gradually as people retire but there's a capital accumulation that does not change since anyone who retires gets replaced by a new employee which will pay the same contributions. Do the companies have any authority to use this money? For example to invest in some other companies to make the accumulation bigger? Can they get interest on this money and possibly use it for themselves without giving it back to employees? Or do they pay the accumulated money plus the interests to them?

I'm not a native English speaker so it is possible that I misused some terms here but I hope it's understandable.

There are two main types of pensions to consider in answering your question:

(1) Defined Benefit pension plan. This type is the 'traditional' pension plan. It means that when you retire, you get a benefit based on, generally, years of service & salary over that period. Even if the market fails, the company still has a legal obligation to pay out the pension, and depending on jurisdiction, probably there is even some form of insurance / protection to try and keep the pension plan paying out, even if the company itself fails. The company likely has a legal obligation to keep the pension plan well-funded, meaning it can't just use new contributions from new employees to pay out retirees - if the market returns on the invested 'pot' are poor, the company will need to contribute additional money to allow for future amounts to be paid properly.

This type of plan works by having employees pay into the 'pension pot', and the company invests that money, plus additional money contributed by the company directly, into the market. If all goes well, the originally invested money will grow, and be able to pay for retirement. If the investments under-perform, the company will need to pay for any shortfall. This places the risk of market failure on the company, not the individual (except in case of complete uninsured bankruptcy, in which case the retirees might lose everything).

(2) Defined contribution pension plan. This type is becoming more common, because of the risks associated with the defined benefit plan. Here, the employee contributes money to their own personal 'pension pot', and the employer likely puts in some money as well. It is then up to the individual to choose how to invest that money [quite likely there is a limited number of options to choose from, decided by the company when they set up the plan].

Here, things work partly as you are guessing - the money invested earns interest, dividends, and capital returns, based on where the money is invested. However note that new employee contributions are for those new employees only - no one else pays for retiree payments once the company has put in the initial contributions. The risk of the market under-performing, is therefore placed on the individual; the company bears no risk of market failure.

There is a third type of pension plan, government run, which operates by having the whole population pay an additional tax, and pays out from that tax, to all retirees. This operates exactly as you are indicating - new workers effectively pay for the retirees to keep getting their pension. In the case where there are few new workers but many retirees, that can put a severe strain on taxing the smaller group of new workers.

Pension funds are invested, mostly in bonds and equities, and the interest and dividends are added to the funds, which (in the case of defined-benefit pensions) would not be large enough to meet their obligations without the income and capital growth. The money remains in the pension fund and can't be used by the company (except that if the pension fund runs a surplus, the company may be able to reduce or pause its payments into the fund).

But my question is, that this pension fund is basically a bank account, and does this account get interest over the years?

This is likely to be a misconception on your part. The money that is paid into a pension "pot" is almost certainly invested by the pension company into equities, bonds and other securities. As such, there is very little cash sitting there; it does not really act like a bank account but more like a normal shares/investment account.

The total value of the account will (usually) increase due to dividends from the equities, coupon interest from the bonds, and capital growth (change in prices). But this isn't really the same thing as the interest you'd get if you put the same money in a bank account.

Note that there are several different types of pensions available; I've assumed here that we're talking about Defined Contribution which is the only one that has a concrete "pension pot". Others don't even have that - you just pay someone money every month in exchange for a promise for them to pay you more back in future.

It's also worth noting that the details will depend on whoever is providing your pension, and the rules around pensions in your country. Theoretically, a bank could provide a high-interest cash savings account within a pension wrapper (i.e. a pension that doesn't invest in any securities, but just pays a set amount of interest on the cash). However, this would very likely be a bad idea for both the bank and its customers as cash is a terrible vehicle for long-term growth.

(If you had any follow-up questions, it would be good to be more specific about the situation you're thinking of.)

Stocks and bonds behave differently over decades

A pension fund is a lot like a university endowment - it is a pot of money that will exist for a very long time. Because of that, the rules of investment change.

Look at history for how stocks perform over a 5 year period. Some 5-year windows are good, some are bad. Very few are terrible.

Now stretch the window to a 30 year period. They're all good. Every single one. In the long run, the stock market always wins.

I manage endowments. These are huge pots of money which are supposed to earn income: interest, dividends, capital gains. We recently had a rules change in endowments: they used to be very complicated. Now you are obliged to invest for growth and take only 4-7% per year, but can do that in good times and bad.

What is growth, for an endowment or pension fund? It is that 30-year thing, where you get the most earnings over the very long term. You are required to invest there, and you'll be sued if you do not.

Growth has a partner: wherever there is growth, there is volatility. You call it "risk".

And because of that "risk", you are very reluctant to invest in the stock market, not even even over the very long term, where that "risk" disappears into the gains.. And so, you can't fathom the idea that a pension fund would do that. It does, and this works.

A few pension funds get very activist with their investments, and make bold (stupid) investments. At this tier of investing, bold==stupid. The #1 mistake is investing in their own company's stock, because now all your eggs are in one basket: if the company flounders and employees want to retire instead of seek new work, the retirement money isn't there. This is dirty dealing: the funds manager bought the stock because he's buddy-buddy with the business managers, who needed the infusion of capital because the business is being mismanaged. That must be illegal, it surely would be for an endowment manager.