# APR / APY calculations
{% hint style="warning" %}
The formulas below are provided for educational and informational purposes. Any past performance is historical and not indicative of future results. Any use of decentralized finance involves various significant financial risks; always Do Your Own Research (DYOR).
{% endhint %}
## Stability Pool staking
### **APR for INDY rewards**
*Averaged over the prior epoch*
#### **Formula**
$$
APR\_t = \frac{c\_{t-1} \* d\_{t-1}}{a\_{t-1} \* b\_{t-1}} \* 365 \* 100
$$
Where
* `t` is the day at which the calculation is performed
* `a` is the amount of a given iAsset staked in a Stability Pool
* `b` is a given iAsset price at daily close, denominated in ADA
* `c` is the daily amount of INDY awarded to a given iAsset’s Stability Pool
* `d` is the INDY price at daily close, denominated in ADA
### **APR for ADA rewards**
*Averaged over a period of last 3 months or over a period spanning from the day of iAsset launch till the day of reward calculation, whichever is shorter.*
#### Formula
$$
v = a - b \* c
$$
$$
\mu = \frac{\sum\_{i=1}^nx\_i}{n}
$$
$$
APR = \frac{\sum\_{i=1}^{|n|}v\_i}{\mu} \* \frac{365}{n} \* 100
$$
Where
* `n` is min\[90, number of days from iAsset launch to the day of calculation]
* `v` is a set comprising values gained from liquidated CDPs over ‘n’ days, denominated in ADA
* `a` is the amount of collateral from a liquidated CDP, denominated in ADA
* `b` is amount of iAsset burned from a liquidated CDP
* `c` is the Oracle Price of the iAsset from a liquidated CDP taken at the time of liquidation, denominated in ADA
* `μ` is the average value staked in the iAsset’s Stability Pool over `n` days, denominated in ADA
* `x` is a collection of total value staked in an iAsset Stability Pool, denominated in ADA and covering a period of n days
## Liquidity Pool Tokens staking
### **APR for INDY rewards**
*Averaged over the latest epoch*
#### Formula
$$
APR\_t = \frac{c\_{t-1} \* d\_{t-1}}{2\*a\_{t-1} \* b\_{t-1}} \* 365 \* 100
$$
Where
* `t` is the day at which the calculation is performed
* `a` is the amount of a given iAsset locked across all DEXs
* `b` is the iAsset price at daily close, denominated in ADA
* `c` is the daily amount of INDY awarded to LP stakers of a particular iAsset
* `d` is the INDY price at daily close, denominated in ADA
## INDY staking
### **APR for INDY rewards**
***Based on the latest epoch***
#### Formula
$$
APR = \frac{b}{a} \* y \* 100
$$
Where
* `a` is the amount of INDY staked at a particular epoch
* `b` is the amount of INDY awarded to INDY stakers at a particular epoch
* `y` is a constant representing the number of Cardano epochs in a year (fixed at 73)
#### Considerations
The APR value can only be computed once per epoch (every 5 days), given the amount of INDY awarded to INDY stakers can only be determined at the end of an epoch.
### **APY for INDY rewards**
***Based on latest epoch***
#### Formula
$$
APY = ((1 + \frac{APR}{y\*100})^y - 1) \* 100
$$
Where
* `APR` is the estimated annualized return for INDY stakers
* `y` is a constant representing the number of Cardano epochs in a year (fixed at 73)
### **APR for ADA rewards**
*Based on last 30 days*
#### Formula
$$
v = a \* (\frac{b}{c})
$$
$$
APR = \frac{\sum\_{i=1}^{|v|}\*v\_i}{s} \* 12 \* 100
$$
Where
* `v` is a set comprising the value of ADA distributed in a day, over a period of the last 30 days and denominated in INDY
* `a` is the amount of ADA distributed in a day
* `b` is the daily close price of ADA, denominated in USD
* `c` is the daily close price of INDY, denominated in USD
* `s` is the average amount of INDY staked for the last 30 days
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