Bitcoin Controlled supply

A fixed money supply, or a supply altered only in accord with objective and calculable criteria, is a necessary condition to a meaningful just price of money.[1]
—Fr. Bernard W. Dempsey, S.J. (1903-1960)

In a centralized economy, currency is issued by a central bank at a rate that is supposed to match the growth of the amount of goods that are exchanged so that these goods can be traded with stable prices. The monetary base is controlled by a central bank. In the United States, the Fed increases the monetary base by issuing currency, increasing the amount banks have on reserve, and more recently, printing money electronically in a process called Quantitative Easing.
In a fully decentralized monetary system, there is no central authority that regulates the monetary base. Instead, currency is created by the nodes of a peer-to-peer network. The Bitcoin generation algorithm defines, in advance, how currency will be created and at what rate. Any currency that is generated by a malicious user that does not follow the rules will be rejected by the network and thus is worthless.

Currency with Finite Supply

Block reward halving

Controlled supply
Bitcoins are created each time a user discovers a new block. The rate of block creation is adjusted every 2016 blocks to aim for a constant two week adjustment period (equivalent to 6 per hour.) The number of bitcoins generated per block is set to decrease geometrically, with a 50% reduction every 210,000 blocks, or approximately four years. The result is that the number of bitcoins in existence is not expected to exceed 21 million.[2] Speculated justifications for the unintuitive value "21 million" are that it matches a 4-year reward halving schedule; or the ultimate total number of Satoshis that will be mined is close to the maximum capacity of a 64-bit floating point number. Satoshi has never really justified or explained many of these constants.
ControlledSupply.png

This decreasing-supply algorithm was chosen because it approximates the rate at which commodities like gold are mined. Users who use their computers to perform calculations to try and discover a block are thus called Miners.
See also: https://bashco.github.io/
Projected Bitcoins Short Term
This chart shows the number of bitcoins that will exist in the near future. The Year is a forecast and may be slightly off.

• In Block 124724, user midnightmagic mined a solo block to himself which underpaid the reward by a single Satoshi and simultaneously destroyed the block's fees. This the the only known reduction in the total mined supply of Bitcoin. Therefore, from block 124724 onwards, all total supply estimates must technically be reduced by 1 Satoshi.

Projected Bitcoins Long Term

Supply timeline estimation
Because the number of bitcoins created each time a user discovers a new block - the block reward - is halved based on a fixed interval of blocks, and the time it takes on average to discover a block can vary based on mining power and the network difficulty, the exact time when the block reward is halved can vary as well. Consequently, the time the last Bitcoin will be created will also vary, and is subject to speculation based on assumptions.
If the mining power had remained constant since the first Bitcoin was mined, the last Bitcoin would have been mined somewhere near October 8th, 2140. Due to the mining power having increased overall over time, as of block 367,500 - assuming mining power remained constant from that block forward - the last Bitcoin will be mined on May 7th, 2140.
As it is very difficult to predict how mining power will evolve into the future - i.e. whether technological progress will continue to make hardware faster or whether mining will hit a a technological wall; or whether or not faster methods of SHA2 calculation will be discovered - putting an exact date or even year on this event is difficult.
The total number of bitcoins, as mentioned earlier, has an asymptote at 21 million, due to a technical limitation in the data structure of the blockchain - specifically the integer storage type of the transaction output, this exact value would have been 20,999,999.9769 bitcoin. Should this technical limitation be adjusted by changing the width of the field, the total number will still only approach or be a maximum of 21 million.

Note: The number of bitcoins are presented in a floating point format. However, these values are based on the number of satoshi per block originally in integer format to prevent compounding error.

• In block 124724, user midnightmagic solo mined a block which caused one less Satoshi to be created than would otherwise have come into existence. Therefore, all calculations from this block onwards must now, to be accurate, include this underpay in total Bitcoins in existence.

What happens when all the bitcoins are mined?
The bitcoin inflation rate steadily trends downwards. At the time of writing, more than 3 out of every 4 bitcoins that will ever exist has already been mined, and the annual inflation rate is just 4%. The block reward given to miners is made up of newly-created bitcoins plus transaction fees. As inflation goes to zero miners will obtain an income only from transaction fees which will provide an incentive to keep mining to make transactions irreversible.
Due to deep technical reasons, block space is a scarce commodity, getting a transaction mined can be seen as purchasing a portion of it. By analogy, on average every 10 minutes a fixed amount of land is created and no more, people wanting to make transactions bid for parcels of this land. The sale of this land is what supports the miners even in a zero-inflation regime. The price of this land is set by demand for transactions (because the supply is fixed and known) and the mining difficulty readjusts around this to keep the average interval at 10 minutes.