Understanding Compound's Interest Rate Model in DeFi

Introduction to Compound

Compound is a decentralized lending protocol built on Ethereum smart contracts. Unlike traditional centralized finance, Compound offers transparent interest rate models, enhanced privacy, instant borrowing, and flexible lending terms without lock-in periods.

Core Architecture of Compound

Let's examine the structure using DAI (currently offering the highest lending APY) as an example:

1. Lenders deposit DAI into smart contracts to immediately start earning interest
2. Borrowers can withdraw DAI by collateralizing other assets (e.g., ETH)

3. Key features:

   • All loans are over-collateralized (total collateral > borrowed amount)
   • Interest payments are distributed proportionally among all lenders
   • Both lenders and borrowers can withdraw/repay funds at any time

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The cToken Mechanism

When lenders deposit 1 DAI, they receive cDAI (compound DAI) tokens. These tokens represent:

• A claim on the original DAI
• Accumulated interest over time
• The exchange rate between cDAI and DAI increases as interest accrues

Interest Calculation Model

Exchange Rate Components

The conversion rate between cDAI and DAI depends on:

• totalCash: Available DAI in the contract
• totalBorrows: Outstanding DAI loans (principal + interest)
• totalReserves: Protocol reserves (portion of interest set aside)
• totalSupply: Total cDAI in circulation

Practical Example

1. Alice deposits 1,000 DAI → receives 40,000 cDAI (exchange rate: 0.025)
2. After one year → exchange rate increases to 0.0275
3. Alice redeems 40,000 cDAI → receives 1,100 DAI
4. The extra 100 DAI represents interest earned

Interest Rate Determination

Utilization Rate

The primary driver of interest rates is the Utilization Rate:

Percentage of deposited funds currently being borrowed

Borrow APY Formula

Borrow APY = Base Rate + (Utilization Rate × Multiplier)

Components:

• Base Rate (minimum borrowing cost)
• Multiplier (interest sensitivity to utilization)
• Utilization Rate (current borrowing demand)

For DAI:

• Base Rate: 5%
• Multiplier: 12%
• Current Utilization: 62.13% → Borrow APY = 12.46%

Supply APY Formula

Supply APY ≈ Borrow APY × Utilization Rate × (1 - Reserve Factor)

For DAI:

• Reserve Factor: 5%
• Current Supply APY ≈ 7.35%

Rate Parameters Across Assets

Rate Update Frequency

Interest rates update with each new Ethereum block (~15 seconds):

1. Rates recalculate whenever utilization changes
2. Interest compounds every block
3. Annual block count: 2,102,400 (estimated)

Example Calculation

1. Bob borrows 100,000 DAI at 10% APY
2. After 1 hour (240 blocks), rate increases to 15%

3. He repays after 2 hours:

   • First hour interest: ~1.14 DAI
   • Second hour interest: ~1.71 DAI (on new principal)
   • Total repayment: 100,002.85 DAI

Collateral and Liquidation

Key protections for lenders:

1. All loans are over-collateralized
2. Each asset has a Collateral Factor (e.g., ETH = 0.75)

3. If borrowed value exceeds permitted ratio:

   • Up to 50% of debt gets liquidated
   • Liquidators receive collateral at a discount (typically 8-10% bonus)

Key Benefits of Compound's Model

• Instant access: No loan matching required
• Transparent rates: Algorithmically determined by utilization
• Continuous compounding: Interest updates every 15 seconds
• Secure lending: Protected by over-collateralization
• Flexible withdrawals: No lock-up periods

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FAQs

How often does interest compound on Compound?

Interest compounds with each new Ethereum block (~every 15 seconds), making it effectively continuous compounding.

What determines borrowing costs on Compound?

Three factors:

1. Base interest rate (protocol-set minimum)
2. Current utilization rate (demand for borrowing)
3. Multiplier parameter (sensitivity to utilization)

Can I lose money lending on Compound?

Possible risks include:

• Smart contract vulnerabilities
• Collateral depreciation triggering mass liquidations
• However, the over-collateralization mechanism provides substantial protection

How is supply APY calculated?

It's approximately:
(Borrow APY) × (Utilization Rate) × (1 - Reserve Factor)
Where Reserve Factor is the protocol's cut of interest.

What happens if utilization reaches 100%?

At 100% utilization:

• Borrow APY hits maximum (17% for DAI)
• New borrows become impossible until repayments occur
• Existing borrowers can still repay loans

Why do different assets have different rates?

Each market has independent:

• Supply/demand dynamics
• Risk profiles
• Protocol parameters
  Resulting in unique interest rate curves.