The Compound protocol contracts use a system of exponential math, ExponentialNoError.sol, in order to represent fractional quantities with sufficient precision.
Most numbers are represented as a mantissa, an unsigned integer scaled by 1 * 10 ^ 18, in order to perform basic math at a high level of precision.
Interest rates for each market update on any block in which the ratio of borrowed assets to supplied assets in the market has changed. The amount interest rates are changed depends on the interest rate model smart contract implemented for the market, and the amount of change in the ratio of borrowed assets to supplied assets in the market.
See the interest rate data visualization notebook on Observable to visualize which interest rate model is currently applied to each market.
Historical interest rates can be retrieved from the MarketHistoryService API.
Interest accrues to all suppliers and borrowers in a market when any Ethereum address interacts with the market’s cToken contract, calling one of these functions: mint, redeem, borrow, or repay. Successful execution of one of these functions triggers the accrueInterest method, which causes interest to be added to the underlying balance of every supplier and borrower in the market. Interest accrues for the current block, as well as each prior block in which the accrueInterest method was not triggered (no user interacted with the cToken contract). Interest compounds only during blocks in which the cToken contract has one of the aforementioned methods invoked.
Here is an example of supply interest accrual:
Alice supplies 1 ETH to the Compound protocol. At the time of supply, the supplyRatePerBlock is 37893605 Wei, or 0.000000000037893605 ETH per block. No one interacts with the cEther contract for 3 Ethereum blocks. On the subsequent 4th block, Bob borrows some ETH. Alice’s underlying balance is now 1.000000000151574420 ETH (which is 37893605 Wei times 4 blocks, plus the original 1 ETH). Alice’s underlying ETH balance in subsequent blocks will have interest accrued based on the new value of 1.000000000151574420 ETH instead of the initial 1 ETH. Note that the supplyRatePerBlock value may change at any time.
// SPDX-License-Identifier: BSD-3-Clause
pragma solidity ^0.8.10;
/**
* @title Compound's InterestRateModel Interface
* @author Compound
*/
abstract contract InterestRateModel {
/// @notice Indicator that this is an InterestRateModel contract (for inspection)
bool public constant isInterestRateModel = true;
/**
* @notice Calculates the current borrow interest rate per block
* @param cash The total amount of cash the market has
* @param borrows The total amount of borrows the market has outstanding
* @param reserves The total amount of reserves the market has
* @return The borrow rate per block (as a percentage, and scaled by 1e18)
*/
function getBorrowRate(uint cash, uint borrows, uint reserves) virtual external view returns (uint);
/**
* @notice Calculates the current supply interest rate per block
* @param cash The total amount of cash the market has
* @param borrows The total amount of borrows the market has outstanding
* @param reserves The total amount of reserves the market has
* @param reserveFactorMantissa The current reserve factor the market has
* @return The supply rate per block (as a percentage, and scaled by 1e18)
*/
function getSupplyRate(uint cash, uint borrows, uint reserves, uint reserveFactorMantissa) virtual external view returns (uint);
}
Since there is a state variable isInterestRateModel, this contract is an abstract contract instead of an interface.