APY Calculation

Introduction

This document describes how BitFi computes and reports APY for bfBTC. We publish two complementary metrics:

• 7‑Epoch Rolling APY (“7D APY”)

• Cumulative Project APY (since genesis)

Both are derived from the on-chain exchange rate between bfBTC and BTC.

Terminology

• Epoch N: The N‑th rebasing or accounting interval at which the bfBTC/BTC exchange rate is finalized.

• T_N: Unix timestamp (in seconds) when epoch N is finalized.

• R_N: Exchange rate at epoch N, expressed as BTC per 1 bfBTC. In words, “1 bfBTC = R_N BTC.”

• S_year: Number of seconds in one year. Unless otherwise noted, S_year = 31,536,000.

• Percent vs fraction: All APY formulas below return percentage values (i.e., multiplied by 100).

Notes:

• The exchange rate R_N is expected to be non‑decreasing over time if bfBTC accrues yield in BTC.

• Timestamps must be strictly increasing: T_N > T_{N-1}.

7‑Epoch Rolling APY (“7D APY”)

Definitio

A linearized, annualized rate based on the change in the bfBTC/BTC exchange rate over the last seven epochs. Because epochs are not guaranteed to be exactly 24 hours, this “7D APY” can differ from a strict 7‑calendar‑day APY.

Formula

$$\mathrm{APY}^{(7)}(N) = 100 \times S_{\text{year}} \times \frac{\displaystyle \frac{R_{N}}{R_{N-7}} - 1}{\displaystyle T_{N} - T_{N-7}}, \qquad N \ge 7$$

Where:

• R_N / R_{N-7} − 1 is the relative change over the last seven epochs.

• The fraction is scaled to an annual rate by S_year, then converted to percent by 100.

Notes:

• Require N ≥ 7.

• If T_N − T_{N-7} is very small or zero, skip the update or fallback to a safe default.

Cumulative Project APY (since genesis)

Definition

A linearized, annualized rate computed from genesis (epoch 0) to epoch N.

Formula

$$\mathrm{APY}_{\text{cumulative}}(N) = 100 \times S_{\text{year}} \times \frac{\displaystyle \frac{R_{N}}{R_{0}} - 1}{\displaystyle T_{N} - T_{0}}$$

Where:

• R_N / R_0 − 1 is the total relative appreciation of bfBTC versus BTC since genesis.

• Linearization makes the rate easy to interpret and stable across reporting intervals.