Wikipedia:Reference desk/Archives/Mathematics/2021 March 20

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March 20

What would need to be the value of bitcoin halving (instead of default "divided by 2") to make sure the amount of monetary inflation the coin had comparing the end of year 5 with the start of year 5, be less than 2%?

What would need to be the value of bitcoin halving (instead of default "divided by 2") to make sure the amount of monetary inflation the coin had comparing the end of year 5 with the start of year 5, be less than 2%?

Bitcoin has a thing called halving, at the first 4 years at each 10 minutes at average, bitcoin creates 50 new coins, after 4 years, the halving happened and instead of 50 coins, bitcoin would created 25 coins (50 divided by 2), and 4 years after it, the value will be 12.5 (or 25 divided by 2).....

How would the halving need to work (the value of X at "dividided by X") needed to make sure bitcoin would have less than 2% monetary inflation, from start of year 5 to end of year 5, so the amount of bitcoin would increase less than 2% at the fifth year.2804:7F2:68C:C9BA:C5C2:1AD:305D:20A7 (talk) 13:17, 20 March 2021 (UTC)

You didn't mention it, but it's also relevant that at time 0 there were 0 bitcoins in existence. I'm going to simplify things a bit and assume all years are equal length. If there were no halving, the 5th year would increase the number of bitcoins by 25%. You instead want 2%, so you need to divide the generation by 12.5.--2406:E003:E2B:2201:EC74:5CC4:B623:54 (talk) 10:38, 21 March 2021 (UTC)

• The question can be reformulated as follows: on year $N$, I add $C\times r^{N}$ coins; what are the values of $r$ such that the additional amount of coins on year 5 is less than 2% (or more generally, a fraction $f$) of the total of the amount of coins from the previous years?

Asked this way, it is a fairly textbook-y example of a geometric series; see Geometric_series#Closed-form_formula in particular, from which we can deduce that the condition is $r^{4}<f\times {\frac {1-r^{5}}{1-r}}$. Maybe there is an analytical solution (and if there is not, computers can still find the root) but I am too lazy for that. Instead, I say that r is going to be small so the inequality is roughly $r^{4}<f$, from which the answer is $r<f^{1/4}$, or about 37.6% for f=2%.

Please note, however, that the above is entirely disconnected from the common meaning of "inflation", namely that the price of goods in a given currency increases. Indeed, the prevalent view of Bitcoin promoters as far as I understand it is that the crypto recreates the gold standard. The intent is to create a currency that is deflationary in the long run (because the production of goods grows faster than the money supply). Tigraan^{Click here to contact me} 16:05, 22 March 2021 (UTC)