Case 1)
When will the amount of freicoins destroyed by demurrage equal the 1 btc generated per block? [2 btc]
That is, when the total supply of freicoins will converge? [5 btc]
With 52560 new coins per year from mining and a 3% demurrage, the growth of freicoins is defined as such: y' = 52560 * e^(-0.03x)
The total number of freicoins for a given year must then be: y = integrate(y', 0, x)
Using those definitions we can calculate that 50% of the coins will be generated in a little over 23 years, 90% of the coins will be generated in nearly 77 years and it will take 153 years to generate 99% of the coins.
What will be the total amount of freicoins then?
The number of coins produced approaches 1,752,000 as time approaches infinity. To calculate the limit, use this equation: 52560 blocks per year * coins per block / demurrage.
Case 2)
-The total amount of freicoins will converge in 21 millions at the same time that the bitcoin network does (¿2033?).
How many freicoins have to be issued with each block to achieve this? [5 btc]
You can't change both the coin limit (21 million) and when the limit is reached (2033, 21 years from 2012) by only changing how many coins are issued.
By issuing around 25.6 coins per block you will hit 21 million in 21 years but the max number of freicoins will be ~44,900,000. However, with a demurrage of 17% and 70 coins per block, you'll hit 21 million in 21 years with a limit of 21.6 million coins.
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