As an offtopic: That is so funny cause I always considered money, which is basically debt or I Owe You or a Promissory Note, a belief. Their value only exists in the minds of people and they have nothing to do with some natural thing.
Funnier still would be trying to explain to someone to whom you owed money (or apples) that your debt (or their expectation of credit) was merely a belief.
Money is indeed an "IOU" or a promissory note, but it is the promise that matters - not the note. It is what the note promises that matters. Without the promise it is not a promissory note (not "money"). Without the eventual fulfilment of the promise it is not a promise.
Money is a model, and what it models is real. Otherwise it's not a very good model. Not good money.
Well that someone surely will find it strange, except when he realises what he wants in the end is anything but money.
It models a system of beliefs. The simplest example is bitcoin. The first transaction bought a pizza with a bitcoin. A ~year later 1 bitcoin was 1000 dollars .
You exchange it for what other people believe the money's worth. I gave you the simplest example. 1 bitcoin=1 pizza , 1 bitcoin =1000 pizzas or dollars or whatever .Why beliefs? As you suggest, what you want is not money as such, but what it models or what it represents, ie. that for which the money can be exchanged. I suppose if you wanted to exchange it for some belief system you could do that. But there are heaps of other things for which it can be exchanged.
Indeed if you are clever with money you can even exchange it for money (typically more money than you originally had) as your bitcoin example might demonstrate. And if you are really really "clever" you can die with a fortune in the bank, having exchanged it for nothing else but more and more money.
Money is a system of representation. One of the oldest systems of representation - perhaps the oldest.