> For the complete documentation index, see [llms.txt](https://docs.fathom.fi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.fathom.fi/fxd-stablecoin/maths-for-position-safety.md).

# Maths for position safety

For a position to be considered safe, below should hold true.

$$
lockedCollateralAmount \* PriceWithSafetyMargin > DebtShare \* debtAccumulateRate,
$$

where

$$
Price WithSafetyMargin = RawPrice \* LTV
$$

When *RawPrice* is the price of collateral from `PriceFeed` and *LTV* is Loan To Ratio.

In other words

$$
lockedCollateralVaule > debtVault
$$

$$
debtVault = debtShare \* debtAccumulateRate
$$

And `debtAccumulatedRate` is calculated as

$$
debtAccumulatedRate = (1 + interestRate)^{1 / 31,536,000}
$$

since `debtAccumulatedRate` is a second pounding *interestRate*.

#### Position safety calculation model

Please refer to below position safety calculation model.

{% embed url="<https://docs.google.com/spreadsheets/d/1--XSZWeKq2HudwH6Btlg8hSpUuEOFStGYXXUDoOW7Es/edit?usp=sharing>" %}
<https://docs.google.com/spreadsheets/d/1--XSZWeKq2HudwH6Btlg8hSpUuEOFStGYXXUDoOW7Es/edit?usp=sharing>
{% endembed %}