DAWN-651 ⁃ setting correct per-block "continuous inflation" so annual inflation is 5%

[thomasbcox]

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 r_a and r_c be the annual and continuous compounding interest rates, respectively.

In case of annual compounding, an initial sum of 1 grows in one year to
1 + r_a. (1)

Whereas in case of compounding N_c times per year, the same initial sum grows to

(1 + (r_c / N_c) ^N_c. (2)

That is, the sum is multiplied by (1 + (r_c / N_c) each cycle.

In the continuous limit,

N_c → ∞ and

lim _{Nc → ∞} (1 + (r_c / N_c) = e^r_c , (3)

where we use the formula lim _{n → ∞} (1 + (x/*n_))ⁿ = *e^x_ for any real number x.

In order for the two rates to be equivalent, we must have

1 + r_a = e^r_c (4)

or equivalently

r_c = ln(1 + r_a). (5)

For r_a = 5.00% = 0.05, the corresponding continuous rate is

r_c = ln(1.05) ≈ 0.04879.

┆Attachments: inflation.pdf

[thomasbcox]

These calculations were performed by Khaled (@zorba80 ) - entered and formatted by me.

[thomasbcox]

I believe this is proven correct. Closing the issue.

[leo-eosnodeone]

Just to make the formulas correct :