> For the complete documentation index, see [llms.txt](https://docs.wandfi.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.wandfi.io/products/yield-vault-v2/product-description/pricing-mechanism.md).

# Pricing Mechanism

The price formula is:

$$
\text{price}(t) = \frac{1}{\text{rateScalar}(t)} \times \ln\left(\frac{p(t)}{1 - p(t)}\right) + \text{rateAnchor}(t)
$$

* **Normalized time ( t )** ranges from 0 (maturity) to 1.
* **rateScalar**:  rateScalar(t) = ScalarRoot / t, adjusts dynamically to maintain capital efficiency.
* **rateAnchor:** rateAnchor(t) = 1 + (InitialAnchor - 1) \* t, adjusts the expected discount between PT and BT.

**Example**:

Given$$( \text{rateScalar} =100)$$, $$( \text{rateAnchor} = 1.1 )$$， initial PT proportion $$( p\_{\text{before}} = 0.6 )$$

$$
\text{price}\_{\text{before}} = \frac{1}{100} \times \ln\left(\frac{0.6}{0.4}\right) + 1.1 = 1.104055
$$

After swapping 100 BT for PT, assuming  $$p\_{\text{after}} = 0.55$$

$$
\text{price}\_{\text{after}} = \frac{1}{100} \times \ln\left(\frac{0.55}{0.45}\right) + 1.1 = 1.102007
$$

$$
dPT = 100 \times \frac{1.104055 + 1.102007}{2} = 110.3031
$$