Back in May, for example, auctioneers Spink & Son sold an older fiver for an astonishing £16,800, thanks to its A01 000004 serial number and history - it had been given to then-chancellor Anthony Barber.
Often, old bank notes turn up years or even decades after they've gone out of circulation.
"We all seem to do it; whether it's loose change down the back of the sofa or crumpled bank notes tucked inside an old handbag at the back of the wardrobe, we just can't stop collecting cash," says Rosamund Evans of law firm Barker Evans.
"Over the years, when dealing with deceased clients' estates, I've come across everything from jars full of old pennies and £5 notes big enough to wallpaper a room, to bundles of cash hidden in old soap boxes under a sink."
Serial numbers can have a big effect on the value of a note, with those beginning 'A' or 'Z' generally worth the most. But anything unusual - 777777 or 123456, for example - can also bump the value up.
And, naturally, any notes with errors can be worth more than the face value.
Meanwhile, many of the new polymer £5 notes are also worth a lot more than a fiver.
Most valuable of all is a note containing a tiny engraved portrait of Jane Austen, which has been valued at up to £50,000. Three of the four notes engraved by Graham Short have been found, but there's one still on the loose.
Other notable new fivers include those with very low serial numbers; indeed, one beginning AA01 is currently listed on eBay for £3,900.
And don't forget that you'll soon get another opportunity to try and spot a valuable new note. The new polymer £10 note is due to enter circulation on Thursday September 14 - and, no doubt, low serial numbers will again be in demand.
Incredibly valuable coins
Incredibly valuable coins
This Australian coin was the first half crown minted under Edward VII. The price for a Melbourne coin in good condition is particularly high because around half of them were produced with faults. It’s now worth £7,500 and has risen in value some 13,789% since it was first in production
The only half crown on the list gets its position from its rarity value. However, the fact this is a silver coin rather than a gold one does affect its value - so it’s worth £10,500. It’s significantly less than others on the list - but it has still appreciated 79,445%.
This is the newest coin in the top ten, and the first year that sovereigns were produced featuring the Queen. The coin was produced in small numbers for investors - rather than for circulation - so is thought to be worth £12,500, due to its rarity.
This is another collectable gold coin prized for its rarity value. It’s worth £15,000 today and has appreciated 191,716%
This was issued in very small numbers, as it was produced during WWI. As a result, few are available - especially as uncirculated coins - so one in good condition will fetch £16,000.
This is another coin prized for its rarity, thanks to a relatively low number being minted, and more being taken out of circulation during WWI. It’s now thought to be worth £17,000 after appreciation of 42,084%.
This 1926 coin has shot up in value and is now worth £31,500. The rise in value is partly to do with a very low mintage, and partly to do with the fact that people were asked to hand their sovereigns over to be melted down during WWI, which took many of them out of circulation.
This brass threepence from 1937 has benefited enormously from the fact that Edward didn’t stick around for long to get too many coins struck in his image before he abdicated. It is now worth £45,000.
This 1933 penny has seen a stunning appreciation in value and is valued at a whopping £72,000 today. The value is due entirely to rarity. Only around seven British versions of this coin were minted, and were intended for the King to bury under the foundation stones of new buildings. They have been subject to theft, and a few are said to be in private hands now.
This isn’t the oldest coin in the list, but it was produced in a year when all gold coins were recalled and exchanged for paper money - so the vast majority were melted down. Its rarity and popularity puts it head and shoulders above the rest. It is worth an eye-watering £6,500,000, and has increased in value 2,178,885% since it was produced.