Mathematical foundations, formulas, and technical conventions.

FinguruTools adheres to standard actuarial and financial mathematics principles across all calculation engines.

All mathematical logic is implemented with deterministic precision, using standard IEEE 754 64-bit floating-point computation internally and explicit rounding at formatting boundaries.

Amortized loan calculations (including EMI, auto loans, personal loans, and standard fixed-rate mortgages) use the standard annuity formula assuming periodic compounding aligned with repayment intervals.

For a loan principal P, periodic interest rate r (where annual rate is divided by payments per year n), and total payment count N = n * years, periodic payment PMT is computed as:

PMT = P * [ r * (1 + r)^N ] / [ (1 + r)^N - 1 ]

For Canadian mortgages, fixed-rate loans compound semi-annually by statutory convention, producing an effective monthly interest rate r_m = (1 + r_annual/2)^(2/12) - 1.

Compound interest and investment growth models calculate future value based on either discrete periodic compounding intervals (daily, monthly, quarterly, annual) or continuous compounding exponential equations.

For recurring investment contributions (e.g. SIP, 401(k), ISA), future value FV combines compound principal growth with the future value of an ordinary annuity or annuity due:

FV = P0 * (1 + r/n)^(n*t) + PMT * [ ((1 + r/n)^(n*t) - 1) / (r/n) ] * (1 + (r/n) * due_factor)

Tax calculations apply progressive marginal rate brackets with standard allowances, deductions, and bracket thresholds applied sequentially to adjusted taxable income.

For income falling across multiple progressive slabs, tax is computed incrementally per tier rather than applying the top marginal rate to aggregate gross income.

All financial results are rounded to two decimal places (cents, pence, paise, or centimes) at display time to maintain clean financial presentation while preserving internal calculation precision.

Amortization schedules adjust the final payment installment to absorb fractional sub-cent rounding differences, ensuring remaining principal balances resolve precisely to 0.00.