We will never hit the 250m hard cap. When calculating the limit of the sum in the above formula, it will show that we will never print more than 123.333.333 Sushi, ever in existence. It will get very close to it, but never touch it. This because the reduction of emissions is done often enough to never reach that number.
But to give you an estimate, this would be the total number of printed tokens, after the reduction is implemented, at some checkpoints in time:
- 66,774,844.55761 Sushi total tokens printed, after 150 days
- 97,396,609.12312 Sushi total tokens printed, after 300 days
- 111,439,209.61612 Sushi total tokens printed, after 450 days
- 117,878,898.2299 Sushi total tokens printed, after 600 days
- 120,832,025.71245 Sushi total tokens printed, after 750 days
- 122,186,277.82792 Sushi total tokens printed, after 900 days
- 122,807,313.93391 Sushi total tokens printed, after 1050 days
- 123,092,110.12551 Sushi total tokens printed, after 1200 days
I figured we already have about 124 million sushi in circulation, it would be fine if we add 123m more.
If you want, you can play around more with the formula on this site.
Another alternative, if the community agrees, we could reduce the emissions according to this formula
The above will reduce emissions to 86.25% every 31 days and it will never print more than 125m coins.
Also to take into consideration, when we talk about limits of sums, it will take a very long time to get near the total cap that we set as objective, but it will never reach it.