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DAWN-651 ⁃ setting correct per-block "continuous inflation" so annual inflation is 5% #1537
This ticket captures calculations for setting the setting correct per-block "continuous inflation" so annual inflation is 5.00%.
(NOTE: Formatting is correct on GitHub but displays incorrectly on Jira.)
Let ra and rc be the annual and continuous compounding interest rates, respectively.
In case of annual compounding, an initial sum of 1 grows in one year to
Whereas in case of compounding Nc times per year, the same initial sum grows to
That is, the sum is multiplied by (1 + (rc / Nc) each cycle.
In the continuous limit,
Nc → ∞ and
lim Nc → ∞ (1 + (rc / Nc) = erc , (3)
where we use the formula lim n → ∞ (1 + (x/*n_))n = *ex_ for any real number x.
In order for the two rates to be equivalent, we must have
1 + ra = erc (4)
rc = ln(1 + ra). (5)
For ra = 5.00% = 0.05, the corresponding continuous rate is
rc = ln(1.05) ≈ 0.04879.