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DAWN-651 ⁃ setting correct per-block "continuous inflation" so annual inflation is 5% #1537

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thomasbcox opened this issue Mar 5, 2018 · 3 comments

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commented Mar 5, 2018

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
1 + ra. (1)

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

(1 + (rc / Nc) Nc. (2)

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)

or equivalently

rc = ln(1 + ra). (5)

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

rc = ln(1.05) ≈ 0.04879.

┆Attachments: inflation.pdf

@thomasbcox thomasbcox assigned thomasbcox and zorba80 and unassigned thomasbcox Mar 5, 2018

@thomasbcox thomasbcox added this to the Q2, 2018 milestone Mar 5, 2018

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commented Mar 5, 2018

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

@blockone-syncclient blockone-syncclient changed the title setting correct per-block "continuous inflation" so annual inflation is 5% DAWN-651 ⁃ setting correct per-block "continuous inflation" so annual inflation is 5% Mar 5, 2018

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commented Mar 25, 2018

I believe this is proven correct. Closing the issue.

@thomasbcox thomasbcox closed this Mar 25, 2018

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commented May 10, 2018

Just to make the formulas correct :

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