> For the complete documentation index, see [llms.txt](https://dev.spectra.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://dev.spectra.finance/integration-reference/spectra-oracles/deterministic-oracles/linear-discount-model.md).

# Linear Discount Model

The linear discount model is a pricing model for the Principal Token (PT) that assumes the PT discount evolves linearly in time.  At start time, the model prices the PT as its par value discounted by the non-compounded instantaneous rate $$r$$ over the term. At maturity, the model prices the PT at its par value. The model linearly interpolates between those two points. More specifically

$$
P(t,T) = \text{PT.previewRedeem}(1) (1 - \frac{1}{1 + r(T-t)})\frac{t}{T} + \frac{\text{PT.previewRedeem}(1)}{1 + r(T-t)}
$$

where $$\text{previewRedeem(1)}$$ gives the redemption rate of the PT,  $$T$$ is the maturity timestamp, while $$t$$ is the current timestamp.