⚠️ Editorial Draft — Needs Human Verification

This document is an unindexed editorial draft. All claims, numbers, and citations below must be reviewed by a qualified specialist before status is changed to approved.

  • Verify Rule 115BAC rounding under Section 288A and 288B (rounding to nearest ₹10)
  • Verify Indian banking convention for fractional paise in monthly reducing loans

Calculation Methodology & Mathematical Transparency

At AG World Tools, precision is our foundational commitment. Because our tools are used for significant financial decisions—such as taking a 20-year home loan or planning income tax outgo—we do not rely on rough floating-point approximations. Every calculator follows strict, deterministic mathematical specifications.

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1. Zero-Paise Ledger Guarantee & Integer Math

JavaScript floating-point arithmetic is notoriously subject to IEEE 754 precision errors (for example, `0.1 + 0.2 === 0.30000000000000004`). In a 240-month amortisation schedule, cumulative floating-point rounding errors can lead to non-zero closing balances or discrepancies of several rupees.

To eliminate this:

  • All monetary values are converted to Integer Paise (1 Rupee = 100 Paise) before computation.

  • Every monthly period computes:

    • $$\text{Closing Balance} = \text{Opening Balance} + \text{Monthly Interest} - \text{Monthly Payment}$$
  • On the final scheduled month, the system reconciles any sub-paise fractional remainder to ensure the final loan balance is guaranteed exactly ₹0.00.

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    2. Compounding Conventions & Leap Year Handling

    Financial calculations in India follow standard Reserve Bank of India (RBI) and Indian Banks' Association (IBA) norms:

    A. Monthly Compounding (Loans & Fixed Deposits)

    For monthly reducing home and auto loans, the monthly rate $r$ is derived as: $$r = \frac{\text{Annual Nominal Rate}}{12 \times 100}$$

    B. Daily Interest Accrual & Leap Years

    For instruments that accrue daily interest (such as bank savings accounts or short-term deposits):
  • Standard years use a 365-day denominator (`Rate / 365`).
  • Leap years (e.g., 2024, 2028) use a 366-day denominator (`Rate / 366`) during the leap period, preventing leap-day interest drift.

    • C. Quarterly Compounding (Bank FDs & Small Savings)

    Bank Fixed Deposits and post office schemes compound interest at the end of each quarter (every 3 calendar months). The effective compounding factor per quarter is: $$\left(1 + \frac{R}{400}\right)$$

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    3. Statutory Tax Rounding Rules (Income-tax Act, 1961)

    Our tax and salary calculation engines strictly observe statutory rounding rules established under the Indian Income-tax Act:

  • Section 288A (Rounding of Total Income): Total taxable income is rounded off to the nearest multiple of ten rupees. If the last digit is five or more, it is rounded up; otherwise, it is rounded down.

  • Section 288B (Rounding of Tax Payable/Refundable): The final net tax payable (including surcharge and 4% Health & Education Cess) or refundable is rounded off to the nearest multiple of ten rupees.

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    4. Open-Source Verification

    All mathematical calculation modules are open, transparent, and inspectable in your browser's Developer Tools under `/assets/js/calculations.js`. We invite developers, chartered accountants, and mathematicians to review our formulas.