How to Calculate Historical Interest Rates on Aave, Compound, and Euler
A guide for crypto borrowers and depositors. Learn how to accurately track your DeFi APR and APY.
Why Calculate Your Historical Interest Rate?
Whether you're lending or borrowing on platforms like Aave, Compound, or Euler, knowing your historical interest rate helps you clearly understand your gains or interest owed over time. While you could simply average historical rates from platforms like Aavescan, DefiLlama, Token Terminal, and Dune Analytics, using the interest index provides the most precise calculation.
Two Ways to Calculate DeFi Interest Rates
1. Average the Historical APR from Data Sources
You can take an average of the historical APRs listed on data sources like Aavescan. This is quick and straightforward but doesn't fully account for compounding effects.
2. Use the Protocol's Interest Index (Recommended)
The most accurate method for calculating historical interest involves using the protocol's interest index, such as Aave's liquidityIndex for deposits or variableBorrowIndex for borrows. This method precisely captures compounded interest and all associated fees.
What is the Interest Index?
The interest index (such as Aave’s liquidityIndex or variableBorrowIndex) is a number that continuously increases to reflect accumulated interest. By comparing index values from different dates, you can precisely calculate the interest you've earned or owe, fully accounting for compounding and protocol-specific fees.
Calculating Interest Using the Index
To find your accurate historical interest:
- Locate your initial interest index value (available from Aavescan CSV data or directly from Aave contracts).
- Find the current value of the same index.
- Divide the current index by the initial index, subtract 1, and then multiply by your original deposit or borrowed amount.
The resulting number reflects your total interest earned or owed, fully accounting for compounding and additional fees or rewards.
Interest Rates Deep Dive
Aavescan Pro Research Article - Published 07.11.2022Different techniques for calculating interest rates produce different results, though the index is the most accurate measure for historical periods.
How Compound Lending Rates Work
In Compound V1 and V2, interest accrues every block. However, it only compounds when users interact with the market (lend, borrow, repay, withdraw). Quiet assets might go days without compounding.
Interest between interactions grows linearly. You can read more in the Compound contract code.
Continuous compounding (like Euler) adds little yield but increases gas costs. Below are APY differences based on compounding frequency:
| APR (%) | APY (Daily Compounding) | APY (Per-Second Compounding) |
|---|---|---|
| 1 | 1.005% | 1.005% |
| 5 | 5.127% | 5.127% |
| 150 | 346.79% | 348.17% |
How to Calculate APR and APY for Compound V2
blocksPerYear = 7200 * 365apr = (borrowRatePerBlock / 10^18) * blocksPerYearapy = Math.pow((apr / periods) + 1, periods) - 1
Block Frequency Impact on APR
| borrowRatePerBlock | APR (5000 blocks/day) | APR (7200 blocks/day) |
|---|---|---|
| 10,000,000,000 | 1.825% | 2.63% |
| 50,000,000,000 | 9.13% | 13.14% |
Compound V3 rates are quoted per second. It uses similar compounding rules as V2.
How Aave Lending Rates Work
Aave V2 and V3 use APRs that accrue every second. Borrow interest compounds every second automatically. However, deposit interest only compounds when the market is updated, typically when users interact with it.
Depositors also receive additional yield from flash loan fees.
How to Calculate Aave Deposit APY
depositApr = (liquidityRate / 10^27) + flashLoanFeeBonusdepositApy = Math.pow((depositApr / periods) + 1, periods) -
1
How Euler Lending Rates Work
Euler offers the most predictable compounding. Both borrow and deposit interest rates accrue and compound every second. This eliminates guesswork in APY calculations.
How to Calculate Euler APY
apr = (interestRate / 10^27) * secondsInYearapy = Math.pow((apr / secondsInYear) + 1, secondsInYear) - 1
For a deeper dive, check the Euler contracts.
Special thanks to @samlafer for insights in this Twitter thread and to Robert L. in Compound’s Discord.
Join the discussion on Aavescan Discord.