Transparent by design
Calculation methodology
Every result uses the assumptions shown in its calculator. Finance Sparrow keeps calculation rules separate from predictions and shows the calculation version used by each Beta workspace. A visible version identifies the model; it does not by itself establish independent review or production readiness.
Investment projections
Expected investment returns are entered as yearly rates and converted to a monthly rate with (1 + annual rate)^(1/12) − 1.
Contribution timing. Monthly investments (SIP contributions) can be added at month start (contribute, then earn return) or month end (earn return, then contribute). The Investment Growth calculator defaults to month end.
Fees. Two choices are available: subtract the fee from the expected yearly return before growth—the default—or charge a percentage of the portfolio each month with balance × (1 − fee/12).
Monthly vs one-time investment. The optional comparison uses the same total amount invested over the horizon, then plots both paths. It is educational about contribution timing—not a forecast of which strategy “wins” in markets.
Inflation and today’s value
Future values are discounted by (1 + inflation)^years to estimate purchasing power in today’s money. Goal amounts marked as “today’s money” are inflated forward using the same convention.
Goal Planner
Required contribution finds the starting monthly investment (SIP, with an optional yearly step-up) needed to meet the future target. Time to goal checks each month to find the earliest date that clears the target; when the goal is in today’s money, that future cost grows with the time needed. Fees and contribution timing use the same accumulation conventions as Investment Growth (Goal defaults to 0% fee).
Retirement planning
Two stages. Accumulation uses its own annual return, effective AUM fee and beginning/end contribution timing. Drawdown has separate return, fee and withdrawal timing. Today’s monthly expenses inflate to the selected retirement age, then increase after each 12 retirement months. The declared lifespan sets the exact drawdown horizon.
Required corpus. The target is solved by substituting candidate starting balances into the complete monthly drawdown ledger. Retirement income phases reduce portfolio requests; signed one-time events add or spend cash; reserve and legacy targets must remain satisfied. The expenses ÷ withdrawal-rate value remains visible only as a labelled comparison and is not the model authority.
FIRE and Coast. FIRE checks candidate ages month by month and reports an age only after the complete lifecycle at that age is funded. Coast substitutes zero recurring contributions and zero contribution growth. Lean, Regular and Fat are editable expense scenarios, not hidden multipliers.
Withdrawal planning
Fixed projection uses the entered portfolio and spending. Longevity returns the exact first unmet-cash-flow month or an explicit not-reached state inside the declared horizon. Required corpus and maximum starting withdrawal use expanding bounds and accept a solution only after its substituted ledger has no depletion, no reserve breach and an ending balance at or above the legacy target.
Every month applies beginning one-time events and any beginning-timed withdrawal, effective monthly return, effective monthly AUM fee, then ending events and any end-timed withdrawal. Income phases are bounded by month and may increase annually. Negative event amounts spend from the portfolio; positive amounts add cash. Nominal values are the ledger authority; today’s-money presentation deflates them without changing the model or exported bytes. Smooth returns are not a guaranteed safe withdrawal rate.
Loans
The schedule supports monthly, fortnightly, or weekly payments. The nominal yearly rate is divided by 12, 26, or 52 respectively. Each period applies a rate change, a before-interest prepayment, interest, the scheduled payment, a recurring extra payment, then an after-payment prepayment. The scheduled payment is held fixed; a rate change does not recast it.
Payment mode solves the scheduled payment. Affordable-principal mode expands and bisects a principal bound, then substitutes the result into the entered term. Term mode runs the entered target payment to an exact payoff period. Purchase price − down payment + financed fees is the original principal. Lender rounding, insurance, taxes, penalties, recast rules, and day-count conventions are omitted.
CAGR, ROI and XIRR
Returns Analyzer is the backward-looking twin of Investment Growth: it measures what a path earned from your inputs, rather than projecting a future balance from an assumed rate.
CAGR smooths a single start and end value across a numeric holding period ((ending ÷ starting)^(1 ÷ years) − 1). It ignores intermediate cash flows. ROI is total gain relative to cost and ignores time—prefer CAGR when you know the holding period. Dated holding mode derives the period from exact UTC date-only values. XIRR accounts for dates: it finds the yearly return at which explicit Investment, Proceeds, and Fee rows balance (365-day year). Invalid visible or imported rows reject the whole result; multiple or indeterminate roots never become a selected annual return.
Real annual return uses (1 + nominal) ÷ (1 + inflation) − 1. Benchmark difference is an annual percentage-point comparison. For start/end modes, gross-before-fees adds entered fees back to the ending value; for XIRR it removes explicit Fee rows and resolves again. These conventions measure entered historical results and do not forecast future performance.
Review and corrections
Retained model tests cover selected zero-rate, known-answer, and boundary cases. Each workspace remains Beta while semantic browser journeys, independent numerical review, manual accessibility review, and Oracle ARM64 acceptance are pending. The calculation version changes when a formula or meaning changes. Regulated rates and tax rules are added only with a country, source, effective date, review owner, and review date.