Core Contracts

Summary

The calculateCompoundedInterest function uses a Taylor series expansion for interest calculation, while calculateLinearInterest follows a simple linear formula. This inconsistency can cause the interest collected from borrowers to be insufficient (or excessive) to pay lenders, potentially leading to liquidity imbalances.

Impact

• Underestimation of Interest: Due to precision loss and differences in calculation methods, the interest charged to borrowers may be lower than necessary, leading to insufficient liquidity for lenders.

• Overestimation of Interest: In some scenarios, the compounded calculation may result in higher interest charged to borrowers, leading to unfair borrowing costs.

• Potential Insolvency Risks: If interest collected from borrowers is insufficient to pay the promised returns to lenders, the protocol may face liquidity issues.

Vulnerable Functions

1. calculateLinearInterest(uint256 rate, uint256 timeDelta, uint256 lastIndex)

   • Uses a simple linear formula:

     uint256 cumulatedInterest = rate * timeDelta;

     cumulatedInterest = cumulatedInterest / SECONDS_PER_YEAR;

     return WadRayMath.RAY + cumulatedInterest;

   • This does not compound the interest, leading to a mismatch when compared with the borrower-side calculations.

2. calculateCompoundedInterest(uint256 rate, uint256 timeDelta)

   • Uses a Taylor series expansion to approximate compound interest:

     uint256 ratePerSecond = rate.rayDiv(SECONDS_PER_YEAR);

     uint256 exponent = ratePerSecond.rayMul(timeDelta);

     return WadRayMath.rayExp(exponent);

   • This results in compounded interest, making the effective rate differ from the lenders' linear rate.

Root Cause

• The protocol applies linear interest for lenders while using compounded interest for borrowers.

Reproduction Steps

1. Set rate = 10% (expressed in RAY) and timeDelta = 1 year.

2. Compute calculateLinearInterest(rate, timeDelta, lastIndex).

3. Compute calculateCompoundedInterest(rate, timeDelta).

4. Compare results: The compounded interest will typically be higher than the linear interest.

Recommendation : Use the Same Interest Calculation Method

• Ensure that both lender and borrower interest use the same formula (preferably compounded).

• Update calculateLinearInterest to use WadRayMath.rayExp to match calculateCompoundedInterest.