Some of this I'm paraphrasing from articles; other parts are my own thoughts. I will source as needed. Anyhow. . .
Economics in the Wizarding world is confusing! First, we know that Gringotts is the only bank in Potterverse (and I'm not keen to argue about the plausibility factor of there being only one Wizarding bank in the world; I'm just sayin' -- canon says so, so let's just take it at face value for purposes of answering this question!) and that Gringotts is run exclusively by goblins (canon doesn't indicate who owns Gringotts), an entirely different species than humans. I'll note that Gringotts seems to employ wizards and witches, as both Bill Weasley and Fleur Delacoeur had positions at Gringotts during the series, and that the year three W.O.M.B.A.T. exam that appeared on J.K. Rowling's website on 06.13.07 indicated that the decision to leave Gringotts under the exclusive control of goblins occurred in 1865.
I do not see evidence in canon that formal interest is either distributed or collected within the Wizarding world. ETA: Page 634, Goblet of Fire, British Hardcover, in the chapter The Beginning, George and Free Weasley tell Harry about Ludo Bagman, who apparently 'borrowed' a lot of gold from goblins to gamble and was unable to pay the goblins back; however, it's not specific as to whether the goblins were representing Gringotts when they made the loan. Interest is not mentioned. (01.19.12) If one looks at canon sideways and squints hard enough, it is possible to discern goblin principles that imply interest-like beliefs/practises in a roundabout way. In Deathly Hallows, Bill Weasley has a talk with Harry about goblins and their beliefs on ownership and treasure:
‘Then I have to say this,’ Bill went on. ‘If you have struck any kind of bargain with Griphook, and most particularly if that bargain involves treasure, you must be exceptionally careful. Goblin notions of ownership, payment and repayment are not the same as human ones.’
Harry felt a slight squirm of discomfort, as though a small snake had stirred inside him.
‘What do you mean?’ he asked.
‘We are talking about a different breed of being,’ said Bill. ‘Dealings between wizards and goblins have been fraught for centuries – but you’ll know all that from History of Magic. There has been fault on both sides, I would never claim that wizards have been innocent. However, there is a belief among some goblins, and those at Gringotts are perhaps most prone to it, that wizards cannot be trusted in matters of gold and treasure, that they have no respect for goblin ownership.’
‘I respect –’ Harry began, but Bill shook his head.
‘You don’t understand, Harry, nobody could understand unless they have lived with goblins. To a goblin, the rightful and true master of any object is the maker, not the purchaser. All goblin-made objects are, in goblin eyes, rightfully theirs.’
‘But if it was bought –’
‘– then they would consider it rented by the one who had paid the money. They have, however, great difficulty with the idea of goblin-made objects passing from wizard to wizard. You saw Griphook’s face when the tiara passed under his eyes. He disapproves. I believe he thinks, as do the fiercest of his kind, that it ought to have been returned to the goblins once the original purchaser died. They consider our habit of keeping goblin-made objects, passing them from wizard to wizard without further payment, little more than theft.’
Deathly Hallows - Pages 417-418 - British Hardcover
As the goblins seem to control the Wizarding banking system, I think this is sufficient information to suggest that the Wizarding economic system is not structured exactly like Muggle society's is. Goblins consider wizards who have goblin-made objects to merely be in possession of those objects; they do not consider those wizards as owning the object, even though payment has been made. Wizards consider the exchange of gold for object as payment in full; goblins consider the exchange of gold for object as 'rent,' which could be extrapolated as a metaphor for interest. Especially since the goblins feel that when the goblin-made object passes from one person to another following death, additional payment should be made.
Importantly, the Wizarding world uses commodity money (meaning it is actually structured from something of value: gold, silver, copper) rather than fiat (paper) money (which is simply a representation of a specific monetary value that we Muggles trust has the value of which it claims). One might consider Wizarding money finite (a galleon is always worth a galleon and that never changes) and Muggle money infinite (a pound is sometimes worth a pound, but it depends on the market and interest, both of which are economic practises the Wizarding world doesn't seem to use). From The World of Harry Potter Can Teach Us a Few Things by columnist Bill Gee:
When one wants to buy something in Diagon Alley, or pay for tuition at Hogwarts School, one goes to "Gringotts", the Wizard Bank, travels to its dungeons to the family vault, and withdraws a handful of gold coins called "Galleons". What we do not see are the Goblins who run the bank taking handfuls of straw and spinning it into more gold, nor do we see Goblin "Loan Officers" offering a "low-low" rate on a personal line of credit. The money supply is relatively static, which makes the economy quite stable. A Galleon has relatively the same value as it did a thousand years ago, and life seems to go on just fine.
There is no mention of taxation in Potterverse.
Capitalism seems to be represented, ala Weasleys' Wizarding Wheezes and Professor Slughorn's aside that he might get ten galleons a hair when he procures Hagrid's collection of unicorn tail hairs during the Felix Felicis chapter in Half-Blood Prince. In Order of the Phoenix, Ravenclaw Eddie Carmichael sells a memory-enhancing potion to the fifth years who are revising for their O.W.L.s (apparently it's a worthless potion, though!). Etc.
Frankly, indentured servitude is represented by the house-elves, which is parallel to Muggle economies that rely on sinfully low wages for labour that the majority of the population either won't do for less than a particular wage and/or openly exploit disadvantaged and disempowered populations as part of the structure of what they see as a valid business model (I'm not here to argue the ethics of this; I'm merely presenting this factually). Wherever there is slave-labour, the economy is going to be effected by that, in theory positively.
There is fake money -- Leprechaun's gold -- in the Wizarding world, which is without value much in the same way counterfeited money is in the Muggle world. False or counterfeited money weaving in and out of the economy will affect it in relation to how much profit is lost due to theft; this ultimately, I think, would impact the accuracy of the GNP.
From Exploring the Economic Structure of Harry Potter’s World by Daniel Levy and Avichai Snir of Emory University:
The authors conclude that the Potterian economic model is not a coherent model that fits neatly into one of the standard economic models. Some aspects of the Potterian economy fit well with one type of economic model, while other aspects are consistent with another type of economic model. For example, says Levy, many aspects of the Potterian model that emphasize the problems of inequality as a shortcoming of the capitalist system have Marxian features. At the same time, however, the books frequently adopt a more mainstream “public choice” point of view by portraying the large Potterian government as infested with rent-seeking bureaucrats who limit the spirit of free entrepreneurship and therefore, the ability of individuals to climb up the social ladder.
Could the Geminio Curse be considered a form of interest when applied to gold and treasures in the vaults at Gringotts (ala the Lestranges' vault)? Touching the gold or treasure causes it to multiply infinitely, and canon doesn't address whether the copy holds the same value as the original. ETA: The more I think about it, the less I believe Geminio can be considered an analogy for interest because of what I note below: Conjured items will not last, and treasure and money born from magic count as having been conjured, IMO.
J.K. Rowling does state there are laws legislating what can and cannot be conjured by magic. I'm guessing that conjuring money is a big no-no. Money may also be one of the five exceptions to Gamp's Law of Elemental Transfiguration; the only exception confirmed in canon is food. However, if I were to make a guess, I would postulate money and/or precious metals would be on that list as well. I base this guess on the fact that, according to J.K. Rowling, conjured items are not permanent and eventually disappear, ala Leprechaun's gold.