Finance Calculator
Time value of money with separate payment and compounding frequencies.
Use cash-flow signs: money paid out is negative and money received is positive.
Result
Payment and present/future values use the financial cash-flow sign convention.
How to use this calculator
Use cash-flow signs: money paid out is negative and money received is positive. Enter amounts in the units shown, select the applicable options, and click Calculate. Use Reset to restore the starting values.
Calculation formula
PV × (1+i)^N + PMT × annuity factor + FV = 0.
Assumptions and accuracy
Review timing, rates, fees and result notes when comparing scenarios. Future returns and rates are assumptions rather than guaranteed outcomes. Monetary display follows the currency’s precision; intermediate calculations retain additional digits.
Choose what to calculate
Time value of money calculator with payments
Solve present value, future value, payment, rate or number of periods using signed cash flows. Keep inflows and outflows on opposite signs.
Open this calculationUnderstanding this calculation
Use time-value-of-money modes to solve for future value, present value, payment, interest or period count. Cash-flow signs distinguish money paid out from money received.
Worked examples
Understand cash-flow signs in a TVM calculation
Illustrative inputs are specified in the steps below; the example link loads the complete settings. Unmentioned settings use the linked defaults.
- Two outflows of 100 plus an initial outflow of 1,000 total 1,200 at a zero rate. The balancing future inflow is positive 1,200.
FV: 1,200 USD.
Try these inputsCommon questions
Why are PV and PMT sometimes negative?
A negative sign represents an outflow from the chosen perspective. An initial investment and later proceeds normally have opposite signs.
Is N the number of years?
N is the number of payment periods in this tool. Use payments per year to relate periods to calendar years.
Scope and assumptions
Rates, payment frequency, compounding and timing must be consistent. Numerical solutions may fail for incompatible cash flows.
Sources
- Calculation methodology, rule versions and testing limitations
- Reference calculator for feature comparison (not a model-parity certification)
Calculation notes checked . Examples are mathematical checks under the stated assumptions.
Calculation methods and formulas
Solve FV
Use cash-flow signs: money paid out is negative and money received is positive.
PV × (1+i)^N + PMT × annuity factor + FV = 0.
Solve PMT
Use cash-flow signs: money paid out is negative and money received is positive.
PV × (1+i)^N + PMT × annuity factor + FV = 0.
Solve I/Y
Use cash-flow signs: money paid out is negative and money received is positive.
PV × (1+i)^N + PMT × annuity factor + FV = 0.
Solve N
Use cash-flow signs: money paid out is negative and money received is positive.
PV × (1+i)^N + PMT × annuity factor + FV = 0.
Solve PV
Use cash-flow signs: money paid out is negative and money received is positive.
PV × (1+i)^N + PMT × annuity factor + FV = 0.
See our calculation methodology and review status for data versions, rounding and validation limitations.