aave-protocol-v2/contracts/libraries/MathUtils.sol

// SPDX-License-Identifier: agpl-3.0
pragma solidity ^0.6.8;

import "@openzeppelin/contracts/math/SafeMath.sol";
import "./WadRayMath.sol";

library MathUtils {

    using SafeMath for uint256;
    using WadRayMath for uint256;

    uint256 internal constant SECONDS_PER_YEAR = 365 days;

    /**
    * @dev function to calculate the interest using a linear interest rate formula
    * @param _rate the interest rate, in ray
    * @param _lastUpdateTimestamp the timestamp of the last update of the interest
    * @return the interest rate linearly accumulated during the timeDelta, in ray
    **/

    function calculateLinearInterest(uint256 _rate, uint40 _lastUpdateTimestamp)
        internal
        view
        returns (uint256)
    {
        //solium-disable-next-line
        uint256 timeDifference = block.timestamp.sub(uint256(_lastUpdateTimestamp));

        uint256 timeDelta = timeDifference.wadToRay().rayDiv(SECONDS_PER_YEAR.wadToRay());

        return _rate.rayMul(timeDelta).add(WadRayMath.ray());
    }

    /**
    * @dev function to calculate the interest using a compounded interest rate formula
    * @param _rate the interest rate, in ray
    * @param _lastUpdateTimestamp the timestamp of the last update of the interest
    * @return the interest rate compounded during the timeDelta, in ray
    **/
    function calculateCompoundedInterest(uint256 _rate, uint40 _lastUpdateTimestamp)
        internal
        view
        returns (uint256)
    {
        //solium-disable-next-line
        uint256 timeDifference = block.timestamp.sub(uint256(_lastUpdateTimestamp));

        uint256 ratePerSecond = _rate.div(SECONDS_PER_YEAR);

        return ratePerSecond.add(WadRayMath.ray()).rayPow(timeDifference);
    }

}