For the millionth time, I am working my way through the Harry Potter series, and once again, I found myself asking about how much Harry Potter's fortune is actually worth, and by comparison, the worth of the Weasley family's small savings. My research initially led me to the Harry Potter Lexicon article on Money, which lays out the basics. To quote Hagrid: "The gold ones are Galleons. Seventeen silver Sickles to a Galleon and twenty-nine Knuts to a Sickle, it's easy enough."
The next question is of course exchange rates. While it's not explicitly stated, it seems that the assumption is a fixed rate of exchange between British Pounds and Gold Galleons — five Pounds to the Galleon. Currently, that means that there are roughly $9.50 (American) to the Galleon.
The Lexicon states that "while wizard money seems to be made from actual precious metals, it also seems to have some sort of magic in it which makes it lighter than normal", as a way to explain how Harry is able to easily carry a bag of a thousand Galleons. I disagree entirely. I submit that like most modern money, the Wizarding coins contain some amount of precious metal — either in plating, as part of an alloy, or as a slug that is itself plated.
The fact is, even a small coin weighs at least five grams, or about one sixth of an ounce (Troy) of gold. Gold is currently worth over $600 an ounce. That means that a small coin made entirely of gold (without any magic at all) would be worth closer to $100 — ten times the actual value. And we know that the Wizarding world values gold, as our famed alchemist, Nicholas Flamel, claimed the ability to turn lead into gold as one of the main uses for the priceless Philosopher's Stone.
Therefore, at $634 per ounce for gold, and about 31 grams per Troy ounce, a Gold Galleon would contain less then one half gram of actual gold. Silver is currently priced at $12 per ounce, and at seventeen Sickles to the Galleon, a Sickle is worth about $0.50, and would contain about 1.3 grams of pure silver. And finally, bronze, which is basically worthless at $1.50 per pound, or about $0.10 an ounce. Therefore, considering twenty-nine Knuts to a Sickle, a Bronze Knut is worth a bit less than two cents, which would require about five grams of bronze.
For a bit of reference, I looked on the US Mint site, to get the specifications on modern American coins. A Golden Dollar (which contains not even a microgram of real gold) weighs 8.1 grams, while a Quarter weighs in at 5.67 grams. According to the Mint's site, a 1000-coin bag of Quarters weighs 13.42 pounds. We could assume that a bag of Gold Galleons weighs up to 20 pounds — any more than that and Harry probably wouldn't enjoy carrying it.
Either way, a Gold Galleon would be less than ten percent real gold by mass, a Silver Sickle would be around twenty-five percent silver by mass, and at five grams, a Bronze Knut could actually be worth its weight in bronze.