Plan a known future expense using explicit opening savings, regular contributions, one-offs and a declared return assumption; distinguish full-precision accumulation from a practical posted-cents schedule.
Equal-period equations and practical cash
Start with the amount earmarked for one future expense and the savings already available for it. Payment solves a contribution plan; Future Value projects a contribution you choose; Schedule presents the same goal-solving model with its ledger. The default equal-period model keeps the established end-period nominal-APR equation. A monthly selection divides that annual rate by twelve, while an annual selection uses one period per year. Changing frequency without changing period count changes the horizon.
The practical schedule posts interest and cash to cents, using nearest-cent ties away from zero as an explicit modeling convention. This is not a claim about how a particular bank posts interest. A regular displayed payment can require a changed final payment or a separately identified deadline true-up. For example, twelve zero-rate deposits toward $10,000 use an unrounded payment of $833.3333333333334; the default practical schedule uses eleven deposits of $833.33 and a final $833.37. Existing excess stays in the fund as surplus, with no invented withdrawal. Compare the full-precision and practical views only after reading their labels.
Actual dates and contribution events
Select actual calendar dates when the timing of the expense matters. Enter a start date and deadline rather than treating a number of months as a date. Monthly and annual dates follow the original day and clamp to month-end when needed. Every fourteen days is distinct from twice monthly: the latter uses the fifteenth and month-end. Beginning timing includes the start date and stops recurring contributions before the deadline; end timing starts later and can include the deadline.
Calendar growth uses the equivalent of the entered nominal annual rate over actual days divided by 365. Interest is posted at each grouped event, so this smooth-accrual planning approximation need not match a deposit contract. Contributions on the same date are combined before further growth; their input order cannot invent an intraday advantage. Add one-offs only within the plan and enter nonnegative cents amounts. A past deadline is invalid. A same-day horizon shows immediate funding instead of fictitious future deposits, while an already funded goal retains surplus. The cash ledger identifies regular contributions, one-offs and any deadline true-up separately.
Matched comparisons, outputs and limitations
A frequency comparison needs a declared cash rule. Same total recurring cash redistributes one fixed budget over the alternative contribution dates, with a cents remainder on the last payment. Same amount per contribution instead holds the payment constant and can change total deposits substantially. Both comparisons retain opening savings, one-off times, horizon and equivalent annual growth; neither silently resolves a different target and labels the result a matched budget.
Use the chart to inspect the selected ledger and its goal line, then review individual events and the paginated full schedule. CSV preserves the original period, deposit, interest and balance prefix and appends dates, raw values, allocation and model metadata. Paper limits long schedules to the first two hundred events and says when CSV is needed for the complete ledger. Returns are assumptions, not a savings-product promise; taxes, fees and product restrictions are excluded. Unsupported arithmetic is unavailable rather than a fabricated zero. Ordinary edits stay out of the URL, remembering a plan is optional, and financial sharing requires an explicit reviewed link.