add interest rate and index math + expand ZTokenHarness + introduce accrue interest tests

- Added newBorrowIndex, borrowerDebt, borrowInterestRatePerSecond, and supplyInterestRatePerSecond to InterestMath
- Refactored borrow rate logic to use kink model (utilization threshold) without extra parameters
- Added InterestMath usage inside ZTokenHarness and new view helpers for borrow/supply rate
- Expanded ZTokenTest with AccrueInterest scenarios (no borrow, first borrow, multiple borrows)
- Updated ZToken.tree to include new AccrueInterest branches

Author: ademolahh

src/libraries/InterestMath.sol

@@ -27,31 +27,54 @@ library InterestMath {
         return numerator.divWad(denominator);
     }
 
-    function newBorrowIndex(uint256 currentBorrowIndex, uint256 borrowRatePerSecond, uint256 deltaTime)
+    function newBorrowIndex(uint256 _currentBorrowIndex, uint256 _borrowRatePerSecond, uint256 _deltaTime)
         internal
         pure
         returns (uint256)
     {
         // newBorrowIndex = currentBorrowIndex * (1 + borrowRate * deltaTime)
-        uint256 simpleInterestFactor = borrowRatePerSecond.mulDiv(deltaTime);
-        return currentBorrowIndex + currentBorrowIndex.mulDiv(simpleInterestFactor);
+        // newBorrowIndex = currentBorrowIndex + (currentBorrowIndex * borrowRate * deltaTime)
+
+        return _currentBorrowIndex + _currentBorrowIndex.mulWad(_borrowRatePerSecond * _deltaTime);
+    }
+
+    function borrowerDebt(uint256 _principal, uint256 _currentBorrrowIndex, uint256 _snapshotBorrowIndex)
+        internal
+        pure
+        returns (uint256)
+    {
+        // _principal * _currentBorrrowIndex / _snapshotBorrowIndex
+
+        return (_principal * _currentBorrrowIndex) / _snapshotBorrowIndex;
     }
 
     function borrowInterestRatePerSecond(
         uint256 _utilization,
         uint256 _utilizationThreshold,
         uint256 _baseRatePerYear,
         uint256 _slopeBeforeKink,
-        uint256 _slopeAfterKink,
-        uint256 _kink
+        uint256 _slopeAfterKink
     ) internal pure returns (uint256) {
         uint256 baseRatePerSec = _baseRatePerYear / 365 days;
         if (_utilization <= _utilizationThreshold) {
             // rb = base rate + s1 * Utilization, u <= uopt
-            return baseRatePerSec + (_slopeBeforeKink.mulDiv(_utilization, WAD));
+            return baseRatePerSec + (_slopeBeforeKink.mulWad(_utilization));
         }
 
-        // rb = base rate + s1 * k + s2(U - K), u > uopt
-        return baseRatePerSec + _slopeBeforeKink.mulDiv(_kink, WAD) + _slopeAfterKink.mulDiv(_utilization - _kink, WAD);
+        // rb = base rate + s1 * k + s2(U - K), u > uopt, where k = utilization threshold(_utilizationThreshold)
+        return baseRatePerSec + _slopeBeforeKink.mulDiv(_utilizationThreshold, WAD)
+            + _slopeAfterKink.mulDiv(_utilization - _utilizationThreshold, WAD);
+    }
+
+    function supplyInterestRatePerSecond(
+        uint256 _utilization,
+        uint256 _borrowInterestRatePerSecond,
+        uint256 _reserveFactor
+    ) internal pure returns (uint256) {
+        // rs  = u * rb * (1-rf)
+
+        if (_utilization == 0) return 0;
+        uint256 rate = _utilization.mulWad(_borrowInterestRatePerSecond);
+        return rate.mulWad(WAD - _reserveFactor);
     }
 }

test/mocks/ZTokenHarness.sol

@@ -1,9 +1,11 @@
 // SPDX-License-Identifier: MIT
 pragma solidity 0.8.30;
 
-import { IZToken, ZToken } from "src/ZToken.sol";
+import { IZToken, ZToken, InterestMath } from "src/ZToken.sol";
 
 contract ZTokenHarness is ZToken {
+    using InterestMath for uint256;
+
     uint256 public cash;
 
     uint256 private constant _TOTAL_SUPPLY_SLOT = 0x05345cdf77eb68f44c;
@@ -32,6 +34,28 @@ contract ZTokenHarness is ZToken {
         }
     }
 
+    // function borrowInterestRatePerSecond(
+    // uint256 _utilization,
+    // uint256 _utilizationThreshold,
+    // uint256 _baseRatePerYear,
+    // uint256 _slopeBeforeKink,
+    // uint256 _slopeAfterKink,
+    // uint256 _kink
+
+    function getBorrowInterestRatePerSecond(uint256 _utilization) external view returns (uint256) {
+        return _utilization.borrowInterestRatePerSecond(
+            UTILIZATION_THRESHOLD, BASE_BORROW_RATE, SLOPE_BEFORE_KINK, SLOPE_AFTER_KINK
+        );
+    }
+
+    function getSupplyInterestRatePerSecond(uint256 _utilization, uint256 _borrowInterestRatePerSecond)
+        external
+        view
+        returns (uint256)
+    {
+        return _utilization.supplyInterestRatePerSecond(_borrowInterestRatePerSecond, RESERVE_FACTOR);
+    }
+
     function getTotalCash() external view returns (uint256) {
         return _getCash();
     }

test/unit/ZToken.t.sol

@@ -111,8 +111,39 @@ contract ZTokenTest is Test {
         assertEq(zToken.getBorrowIndex(), 1e18);
     }
 
-    function test_GetBorrowIndex_WhenThereIsBorrowActivity() external {
-        // it should rise with interest
-        vm.skip(true);
+    function test_AccrueInterest_WhenNoBorrowActivity() external view {
+        uint256 utilization = zToken.getUtilization();
+        uint256 borrowInterestRate = zToken.getBorrowInterestRatePerSecond(utilization);
+        uint256 supplyInterestRate = zToken.getSupplyInterestRatePerSecond(utilization, borrowInterestRate);
+
+        assertEq(borrowInterestRate, zToken.BASE_BORROW_RATE() / 365 days);
+        assertEq(supplyInterestRate, 0);
+    }
+
+    modifier whenThereIsBorrowActivity(uint256 _borrow) {
+        zToken.setTotalBorrow(_borrow);
+        _;
+    }
+
+    function test_AccrueInterest_WhenThereIsBorrowActivity(uint256 _borrow)
+        external
+        whenThereIsBorrowActivity(_borrow)
+    {
+        // it borrow interest rate should be greater than zero
+        // it supply interest rate should be greater than zero
+    }
+
+    function test_AccrueInterest_WhenItTheFirstBorrowActivity(uint256 _borrow)
+        external
+        whenThereIsBorrowActivity(_borrow)
+    {
+        // it borrow index should not change
+    }
+
+    function test_AccrueInterest_WhenThereIsMultipleBorrowActivity(uint256 _borrow)
+        external
+        whenThereIsBorrowActivity(_borrow)
+    {
+        // it borrow index should be greater than zero
     }
 }

test/unit/ZToken.tree

@@ -36,3 +36,14 @@ ZTokenTest::getBorrowIndex
 └── when no borrowing activity
     └── it should match the initial borrow index
 
+ZTokenTest::AccrueInterest
+├── when no borrow activity
+│   ├── it borrow interest rate should be base rate
+│   └── it supply interest rate should be zero
+└── when there is borrow activity
+    ├── it borrow interest rate should be greater than zero
+    ├── it supply interest rate should be greater than zero
+    ├── when it the first borrow activity
+    │   └── it borrow index should not change
+    └── when there is multiple borrow activity
+        └── it borrow index should be greater than zero