# Swap

AuroraSwap provides users a simple way to swap tokens on Aurora via automated liquidity pools. In a swap, one token is sold to buy another token. The rate of the swap is determined by the AMM with the equation:

xβy=kx*y=kxβy=k

Where *x *= the number of $AAA tokens, *y *= the number of $BBB tokens, and *k *is a constant. The trader is charged a 0.3% fee to make a swap.

In Figure 1, a trader is swapping $AAA token for $BBB tokens. The trader sends 100 $AAA tokens to the AMM. A 0.3% fee is applied and 0.3 $AAA tokens are not included in the swap. The remaining 99.7 $AAA tokens are swapped in the AMM to $BBB tokens. Since the AMM will be losing $BBB tokens, it must gain $AAA tokens to keep k constant.

The equation:

(1,000+99.7)β(10βy)=10,000(1,000+99.7)*(10-y)=10,000

(1,000+99.7)β(10βy)=10,000

Can be solved for y to give the number of $BBB tokens that the trader will receive. The 0.3% fee of 0.3 $AAA tokens are directly added to the liquidity pool reserves, slightly increasing the value of k.

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