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Interest Rate Calculation

Untangled Protocol leverages an advanced methodology for calculating interest, employing real-time compounding every second to ensure precise and equitable computations in financial transactions that are executed continuously, 24/7.

Introduction to Interest Calculation​

This section provides a foundational understanding of interest compounding and the distinctions between Annual Percentage Rate (APR) and Annual Percentage Yield (APY). Readers well-versed in these concepts can proceed directly to the detailed on-chain implementation section.

Detailed Example of Compounding Interest​

To align with the instantaneous transaction capabilities of blockchain technology, Untangled Protocol compounds interest every second. Here's how it works in a practical example:

Suppose an investment of 100withanAPRof17.00100 with an APR of 17.00%. Under simple annual compounding, the interest calculation is: 100 × 17.00% = 17.00.Thisresultsinatotalof17.00 . This results in a total of 117.00 at the end of one year.

For monthly compounding, the interest rate per month is 17.00% / 12 = 1.4167%. This rate compounded monthly over a year yields: 100×(1+1.4167100 × (1 + 1.4167%)^12 = 118.39

Compounding every second, the formula adjusts the interest rate to a per-second increment: 100×(1+17100 × (1 + 17%/31536000)^31536000 ≈ 118.53

Here, 31536000 represents the total number of seconds in a year, calculated as: 60 * 60 * 24 * 365 = 31536000

Comparing APR and APY in the Untangled Context​

Annual Percentage Rate (APR) is the nominal yearly interest rate, which does not account for the compounding effects within the year. Annual Percentage Yield (APY) incorporates the effects of compounding, demonstrating a higher return as the frequency of compounding increases. In the provided example, the APR is 17.00%. The APY with monthly compounding is approximately 18.49%, while the APY with second-by-second compounding rises slightly to about 18.53%.

Technical Implementation on Blockchain​

To implement this calculation on-chain, Untangled Protocol uses a ratePerSecond formula that ensures accurate interest accrual over any time span, critical for the continuous transaction environment of blockchain. The formula for this rate is: rate=1+𝑖31536000rate=1+31536000i​Where 𝑖i is the APR expressed as a decimal.

For a principal of $100 and an APR of 17.00%: rate=1+0.1731536000=1.0000000053893rate=1+315360000.17​=1.0000000053893

Applying this rate over one year (or 31,536,000 seconds), the debt calculation would be: 𝐷=100×1.000000005389331536000≈118.53D=100×1.000000005389331536000≈118.53D=100×1.000000005389331536000≈118.53

This approach ensures that Untangled Protocol can deliver precise and consistent financial results, accommodating the rapid dynamics of blockchain transactions effectively.