Daily Interest Calculation

Overview

This guide provides a detailed explanation of how to calculate daily interest on the protocol for each lender in a given borrower pool. The goal is to determine the total amount owed and the total interest accrued over time.

Example with interest overtime breakdown

Definitions

1. Annual Percentage Rate (APR): The yearly interest rate expressed as a percentage.
2. Daily Rate: The daily interest rate calculated from the APR.
3. Investment Amount: The amount of money each lender contributes to the loan.
4. Total Loan Amount: The sum of the initial loan amount and the accrued interest over time.
5. Total Amount Owed to Date: Sum of the initial loan amount and all accrued daily interest.
6. Total Interest Accrued to Date: Sum of daily interests accrued over the period.
7. Liquidation Point: Governance-driven % that represents the maximum allowed LTV at any given point
8. Investment APR: Investment Amount / Requested Amount * Max Tier Interest Rate

1. Loan-to-Value (LTV) Ratio: The ratio of the loan amount to the collateral value.

Formulas

1. Convert APR to Daily Rate: Daily Rate=365APR

   $\text {Daily Rate} = \frac{\text{APR}}{365}$

2. Calculate Daily Interest: Daily Interest = Investment Amount × Daily Rate

   $\text {Daily Interest}= \text {Investment Amount} × \text {Daily Rate}$

3. Accumulate Daily Interest:Total Daily Interest=∑(Daily Interest for each Lender)

   $\text{Total Daily Interest}=∑ (\text{Daily Interest for each Lender})$

4. Update Total Loan

   $\text {New Total Loan Amount}=\text {Previous Loan Amount}+ \text {Total Daily Interest}$

5. Recalculate LTV

   $\text{LTV} = \left( \frac{\text{Total Loan Amount}}{\text{Collateral Value}} \right) \times 100$

Example Calculations

Initial Loan Details

• Collateral Value: $10,000
• Requested Amount: $5,000
• Initial LTV: 50%
• Total Pool APR: 70%

Lender Contributions and APRs

• Lender X:

  • Investment Amount: $2,000
  • APR: 28% (Max → )
  • Daily Rate: $\frac {28}{365} \approx 0.0767$
  • Daily Interest: \text {2000×0.000767}≈\1.5342000$

• Lender Y:

  • Investment Amount: $1,500
  • APR: 21%
  • Daily Rate: $\frac {21}{365} \approx 0.0575$
  • Daily Interest: \text {1500×0.000575}≈\0.8625$

• Lender Z:

  • Investment Amount: $1,500
  • APR: 21%
  • Daily Rate: $\frac {21}{365} \approx 0.0575$
  • Daily Interest: \text {1500×0.000575}≈\0.8625$

  Total Daily Interest

  \text{Total Daily Interest} = \1.534 + $0.8625 + $0.8625 = $3.259$

  Daily Calculation Process

  1. Day 1:

     • Previous Loan Amount: $5,000

     • Total Daily Interest: $3.259

     • New Total Loan Amount: $5,000 +$3.259 = $5,003.26

     • New LTV:

       $\left( \frac{5003.26}{10000} \right) \times 100 \approx 50.03\%$

  2. Day 2:
     • Previous Loan Amount: $5,003.26
     • Total Daily Interest: $3.259
     • New Total Loan Amount: $5,003.26 +$3.259 = $5,006.52
     • New LTV: $\left( \frac{5006.52}{10000} \right) \times 100 \approx 50.07\%$
  3. Continue Daily Calculation:
     • Adding the total daily interest to the previous loan amount and recalculating the LTV until it reaches 100% (Or liquidation point defined by the Governance)