The math is an open book
Every picture comes from the same calculation as its numbers. Change an assumption and the whole result follows.
Simple and compound growth
Rates are entered as percentages and converted to fractions. Simple interest uses the annual rate divided by 12 each month, applied only to the starting amount and later deposits. Earlier interest never earns more interest. Compounding frequency and annual-yield conversion do not apply to simple interest.
Compound interest is added every 1, 3, 6 or 12 months, counting from the start of the scenario. With q compounding periods per year, the periodic rate is annual rate ÷ q for a nominal rate, or (1 + annual yield)^(1/q) − 1 for an effective annual yield.
Between compounding dates, interest accrues each month at the periodic rate divided by the number of months in that period. It applies to contributed money and interest added at earlier boundaries. Pending interest is included in the projected total, including at an unfinished final period, but earns no interest until it is added at the next boundary.
Deposits remain monthly. Beginning-of-month deposits earn interest that month; end-of-month deposits begin earning interest the following month. For monthly compounding, the recurrence is previous balance × (1 + monthly rate) + contribution for month-end deposits, or (previous balance + contribution) × (1 + monthly rate) for month-start deposits.
The starting amount is month zero. Every month counts as 1/12 of a year; actual calendar dates and leap years are not used. Balances are not rounded each month. Counting days, adding interest to the balance and paying interest out are separate rules. A maturity calculation for a bank fixed deposit (FD) or certificate of deposit (CD) needs deposit and maturity dates, the applicable day-count rule, compounding and payout terms, rounding and any tax deductions. Currency does not select these rules.
Savings goals
Savings uses the same simple or compound interest model above. Time-to-goal checks the projected total each whole month, starting with month zero, up to 600 months. That total includes pending interest, so a projected goal date may fall before that interest is added to the balance. An unmet goal with no deposits and no interest growth on existing capital is not reachable under the assumptions. A longer-than-600-month result is identified separately.
For a deadline, the engine searches integer minor units (cents for USD, paise for INR) for the smallest deposit that meets the target. The sufficient-unit check allows at least 0.00000001 of the selected currency or one trillionth of the target for floating-point tolerance. A zero-month deadline with an unmet target has no monthly contribution solution.
Emergency funds
Selected target = monthly essential expenses × selected coverage months. Gap = the larger of zero and target minus existing savings. Coverage = existing savings ÷ monthly essentials, unless essentials are zero, when coverage is not applicable.
No interest is included. With positive monthly saving, time is the gap divided by saving, rounded upward to a whole month. The expense breakdown replaces the single essentials total when enabled.
Budget splits
Percentages must total exactly 100. Income is converted to minor units (cents or paise) and percentages to basis points. Each category receives the floor of its share; remaining minor units go to the largest fractional remainders. Ties go to needs, then wants, then savings/debt repayment.
Zero income produces zero allocations. A template is a hypothetical allocation, not a rule or financial-health score.
Recurring payments
Annual run rate uses 52 weekly, 12 monthly, four quarterly or one annual payment. The annual total is authoritative. Average monthly cost divides it by 12; five-year spending multiplies it by five.
Monthly displays are rounded, so multiplying the displayed monthly average by 12 may not exactly reproduce the annual total. No exact billing dates or price changes are modeled.
Inflation
Future cost = starting amount × (1 + inflation rate)^years. Future purchasing power in today’s currency units = starting amount ÷ the same factor. The fixed nominal sum does not disappear.
The rate is a hypothetical constant assumption. It is not a CPI forecast or a current inflation reading.
Limits and rounding
Amount inputs: 0–100 million (10 crore) in the selected currency, with at most two decimal places. Rates: 0–25% with up to four decimals. Growth: up to 1,200 whole months (100 years). Savings: up to 600 whole months. Growth durations above 50 years are illustrations of fixed assumptions, not reliable long-range forecasts. Inflation: up to 50 whole years. Emergency coverage: 1–36 months. Subscriptions: up to eight items with labels up to 60 characters. Outputs above 1 trillion (100,000 crore) in the selected currency are withheld.
Use plain digits or valid Indian/international comma grouping, with a period for decimals. Currency symbols, magnitude words and exponent notation are rejected. Empty and invalid values pause results. Displayed growth is rounded final minor units minus contributed minor units to keep the breakdown reconciled. These are mathematical estimates, not exact bank-statement forecasts.
Checking the model
The project includes independent reference fixtures, invariant checks and browser journeys. Automated tests check mathematical and interface behavior; they do not constitute professional financial review, legal review or a prediction of future results. See the project QA report for the checks actually run.