How APY is Calculated in Augmented Finance

Dear Augmented Community,

We’ve heard a lot of questions on the APY calculation in Augmented Finance. And first of all, we’d like to thank you for your curiosity and interest in our protocol. We always want to be fair and transparent with our users. Below is the breakdown of the APY calculation formulas for all types of operations in Augmented Finance (supply, borrow, stake agTokens, stake Uni LP, stake AGF).

Supply

Let’s break down the formula to calculate the annual percentage yield for the USDC supply pool.

Supply Base APY

This is the yield that you get in the currency of a supplied asset based on current lending/borrowing activity in the asset’s lending pool. The specific percent depends on the utilization rate of the lending pool (borrowers/suppliers) and type of the curve.

The interest rate curves are linear with a kink. Rates follow 2 slopes: a lower slope before an optimal utilisation level and a steeper slope after that level.

For example, for USDC we use an interest rate curve with the optimal utilization rate of 90%. At current borrowing activity, the base APY for suppliers is 0.00%.

Supply Reward APY

Supply Reward APY reflects the liquidity mining reward yield in AGF tokens that you get for supplying this asset.

This is the formula we use for calculating Supply Reward APY for all pools:

Let’s see how Supply Reward APY is calculated for an USDC supplier:

0.12 AGF/sec (emission rate) * 6.88% (USDC supply share of the total emission) * 31,556,952 (number of seconds in a year) * $2.513 (current price of AGF) / 1 230 000 $ (current total supply for USDC pool) = 53.22% APY

Supply Boost APY

Supply Boost APY reflects the additional liquidity mining reward yield in AGF tokens that you get on top of Supply Reward APY for staking AGF tokens. Get additional rewards (Boost APY) for all types of transactions (supply, borrow, stake) via staking AGF tokens: get xAGF tokens for staking AGF tokens. The longer staking period you choose, the more xAGF tokens you get. You can boost your liquidity mining rewards up to 4x.

E.g. if the Supply Reward APY is 30%, you can get +90% as Supply Boost APY. The sum of Supply Reward APY and Supply Boost APY will be 120%, or 4x larger than Supply Reward APY alone.

The Supply Boost APY is calculated by the formula which can be simplified in the following way:

The more detailed calculation can be found below:

1. User’s share of pool = Tokens [supplied / borrowed / staked] by User / Total tokens [supplied / borrowed / staked] by all users
2. User’s pool reward rate in AGF per second = Pool reward rate in AGF per second * User’s share of pool
3. User’s pool boost rate in AGF per second = User’s pool reward rate in AGF per second * Pool’s boost factor
4. User’s max rate in AGF per second = Share of the total emission for Boost in AGF per second * User’s balance of xAGF / Total supply of xAGF held by all users
5. User’s total rate in AGF per second = min (User’s max rate in AGF per second; sum of User’s pool boost rates in AGF per second)
6. Boost APY % (annualized) = User’s total rate in AGF per second * 31,556,952 [number of seconds per year] * AGF price in USD / Value of User’s operations [supply / borrow / stake agTokens / stake Uni LP] in USD

Borrow

Borrow Base APR is the interest that a borrower pays for taking out a loan in the currency of the loan.

The formulas for Borrow Reward APY and Borrow Boost APY are similar to the ones mentioned for Supply (see above). We can’t stress it enough that right now the borrowers are actually earning more liquidity mining yields than they’re paying the interest in the underlying asset for taking out a loan.

Staking agTokens and Uni v2 AGF-ETH LP tokens

Stake Reward APY

Here’s the breakdown of the Stake Reward APY formula to display the yield in AGF rewards that stakers of Uni v2 AGF-ETH LP get:

0.12 AGF/sec (emission rate) * 10.49% (stake Uni v2 AGF-ETH LP share of the total emission) * 31,556,952 (number of seconds in a year) * $2.513 (current price of AGF) / 46 058 $ (current USD value of all Uni LPs staked) = 2,167% APY

And here’s how the Stake Reward APY for agETH staking pool is calculated (it works the same way for all agToken staking pools):

0.12 AGF/sec (emission rate) * 1.75% (agETH staking share of the total emission) * 31,556,952 (number of seconds in a year) * $2.38 (current price of AGF) / 167 000 $ (current USD value of all agETH staked) = 94% APY

Stake Boost APY

See the explanation for Supply Boost APY above. The formula for Boost APY is similar for all type of operations: supply, borrow, stake agTokens, stake Uni LPs.

Stake AGF

Stake AGF APY formula is the following:

Let’s see how Stake AGF rewards are calculated for a user who stakes 100 AGF for 1 year:

0.12 (AGF emission rate per second) * 5.18% (Share of the total emission for xAGF holders) * 31,556,952 (Number of seconds per year) * $2.5 (Current price of AGF) * 25 xAGF (User’s balance of xAGF) / 4000 (Total supply of xAGF held by all users) / (100 (AGF staked by User) * $2.5 (Current price of AGF)) = 1,225% APY

Note: xAGF stands for staked AGF, it is simply AGF staked for a period of time. xAGF amount is calculated as follows:

1 AGF staked for 4 years = 1 xAGF

1 AGF staked for 1 year = 0.25 xAGF

1 AGF staked for 4 weeks = 0.019 xAGF

1 AGF staked for 1 week = 0.0048 xAGF

The longer you stake AGF for, the more xAGF you receive. Stake 100 AGF for a year and you’ll get 25 xAGF. Stake it up for four years, and you’ll get 100 xAGF. All stake periods are irreversible.

Important: there is no way to predict the exact amount of AGF tokens that you get during the period when your AGF tokens are staked. It depends on various parameters like AGF emission rate, total amount of xAGF held by all users, and others.

Here you can see the data with the current emission rate & rewards distribution for each pool and make your own calculations.

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