# How much will BNT pay for impermanent loss protection?

Bancor is not only a pioneer of automatic market makers, but also proposed a solution for impermanent loss protection for the first time, which has made a huge contribution to the development of defi. So how much should it pay for the impermanent loss protection? Whether new BNT will be issued to the market is a question that many people care about for this IL solution. Now we can mathematically deduce how much will BNT pay for impermanent loss protection? First, let’s review the impermanence loss calculation formula of the xyk model:

Here we take BNT-USDT as an example. Assuming that when the price is P0, the liquidity provider deposits y0 USDT to the bancor protocol to provide single sided liquidity, then Bancor will issue an additional x0 BNT for the liquidity provider to deposit into the liquidity pool of BNT-USDT, and when the price moves to Pn, the liquidity provider withdraws USDT equivalent to y0 and LP fees, then the change in the net value of bancor calculated in BNT is: [(xn-x0) + (yn-y0)/pn] /x0;

The net change in USDT is: [(xn-x0)*pn + (yn-y0)]/y0.

Then the loss rate of impermanent loss protection calculated in USDT is 𝐼𝐿𝑃(𝑈𝑆𝐷𝑇 %)=[(xn-x0)*pn + (yn-y0)]/y0/y0–1

According to

We get:

The loss rate of impermanent loss protection calculated in BNT is 𝐼𝐿𝑃(BNT %)=[(xn-x0) + (yn-y0)/pn]/x0/x0–1

Based the same as above we get:

As can be seen from the above calculation, we can know that no matter whether the price of BNT-USDT rises or falls, BNT needs to bear impermanent loss. We can further observe the size of this loss with specific percentage.

If the price falls by 20% and 75%, then

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