how is the value of banknotes guaranteed?
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By the full faith and credit of the issuing country.
My which, I mean not very guaranteed. The value of currency floats in an open market. That value is set by buyers and sellers in a fluid (aka not guaranteed at all) way.
It’s issued by a country and it will always be worth what it says on it. The nominal value (what it says on it) doesn’t change. But that’s only half the story, as inflation changes what you can actually do with the money.
So the effective value is not actually guaranteed.
It could be pegged to the value of a stable commodity (gold). In thay case, your paper money is technically, if not effectively, redeemable for solid gold. This is quite rare now. The USA came off the gold standard in the 70s.
The alternative is called ‘fiat’ currency (roughly translated as ‘because it is said to be so’). This means that the value of the currency is backed up by the government who issues it. It relies on people’s confidence in the strength of the economy.
The issuing country will accept them as payment for official business, like taxes and fees.
Beyond that, there is usually no legal guarantee that anyone else will accept a given banknote as payment. In a healthy economy, it just makes sense for them to do so. Walmart will accept USD in exchange for a t-shirt because they know that employees and vendors will accept USD in return for labor and products. There’s a lot of inertia in a system like that, so it would take significant economic turmoil for Walmart to start preferring some other form of payment.
And for what it’s worth, it’s usually countries in economic turmoil who start passing more laws about how their currency is to be used – for example by mandating exchange rates or price ceilings for certain goods. It has stopped being a good idea for people to use their currency, so the government hopes they can prop it up with the force of law instead.
It’s guaranteed by each government, which ultimately holds power over the entire country including its industry.
So in a roundabout way, the value of a currency is guaranteed by the value of everything the economy produces or provides.
That’s why the US Dollar has always been internationally valued as a rather stable currency: The US economy is one of the strongest economies in the world and it’s extremely unlikely to collapse entirely. So in turn the US Dollar is extremely unlikely to collapse entirely.
It’s.. not? The value changes over time. You won’t always be able to exchange it for the same amount of goods and services, or foreign currency. But if the value is stable-ish, then you can exchange it for a fairly similar amount of goods and services, or foreign currency, and that’s good enough for most people.
Faith in the stability of the currency… and also because it would be the only accepted tax settlement. Difficult to function in today’s world without incurring a taxable event.
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