> For the complete documentation index, see [llms.txt](https://docs.3jane.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.3jane.xyz/backing/ccl/merchant-discount-factor-rate.md).
# Merchant Discount Factor Rate
3Jane gives you an upfront advance and, in return, buys a fixed specified amount of your future yield. *The Discount Factor Rate (DFR) is a discount that reduces the specified amount if you repay the advance amount early, effectively charging you less. The discount shrinks towards zero over time as the days since funding increases.*
$$
\text{RP}(N) = A \times \left( 1 + \sum\_{n=1}^{N} \text{P}\_{n} \right)\\\[2em]
\text{DFR}(N) = 1 - \frac{\mathrm{RP}(N) - A}{\mathrm{A} \times (F-1)}
$$
$$
\begin{aligned}
N &: \text{days since funding} \\\[2pt]
A &: \text{advance amount at funding} \\\[2pt]
\text{F} &: \text{fixed Factor (set at funding)} \\\[2pt]
\text{RP} &: \text{repurchase amount by day N} \\\[2pt]
\text{DFR} &: \text{discount factor rate by day N} \\\[2pt]
\text{P}\_{n} &: \text{daily pacing increment} \\\[2pt]
\end{aligned}
$$
Each day, a tiny pacing increment is applied:
(1) base factor: the pool’s baseline conditions (utilization)
(2) credit risk factor: your credit risk profile
(3) urgency factor: whether you were late that day
Those three slices add up to your daily fraction Pn.
$$
\begin{aligned}
\text{P}*{n}
&: \text{B}*{n}
\+ \text{C}*{n}
\+ \text{L}*{n} \\\[2pt]
\text{B}*{n} &: \text{implied base apy, expressed as a (1) day factor, pool-wide. Derived from the pool’s utilization curve} \\\[2pt]
\text{C}*{n} &: \text{implied credit risk apy, expressed as a (1) day factor, per-user. Derived from the 3CA algorithm} \\\[2pt]
\text{L}\_{n} &: \text{implied urgency apy, expressed as a (1) day factor, per-user. Applied on days flagged late} \\\[2pt]
\end{aligned}
$$
Note: DFR according to the formula is updated daily (as of 11:59 p.m. UTC). Your real-time DFR (and hence early payoff amount) will be updated to include time elapsed from last day DFR prior to payment.
**Example:**
* Advance: **A = 100,000**
* Factor: **F = 1.15**
* Specified Amount: **A⋅F = 115,000**
| bn | | | | | | |
|---|
| D | Bn | Cn | Ln | Pn | Sum Pn | RP(N) | DFR(N) |
| 1 | 0.000115 | 0.000049 | 0 | 0.000164 | 0.000164 | 100,016 | 99.8904% |
| 2 | 0.000112 | 0.000052 | 0 | 0.000164 | 0.000328 | 100,032 | 99.7808% |
| 3 | 0.000117 | 0.000046 | 0.000136 | 0.000301 | 0.000630 | 100,063 | 99.5799% |
| 4 | 0.000109 | 0.000050 | 0 | 0.000160 | 0.000790 | 100,079 | 99.4731% |
| 5 | 0.000120 | 0.000053 | 0 | 0.000173 | 0.000964 | 100,096 | 99.3571% |
---
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