Time Value of Money Calculator

Solve for present value, future value, payment, rate, or number of periods using a traditional TVM model.

General Planning · Last reviewed: August 8, 2026

On this page

Overview

The Time Value of Money Calculator solves for one unknown in a traditional five-variable TVM relationship: present value (PV), future value (FV), equal payment per period (PMT), rate per period (I/Y), or number of periods (N).

Select the unknown, enter the other four values, and choose whether recurring payments occur at the beginning or end of each period. The result follows the cash-flow signs entered.

Scope and Use

The calculator supports deterministic accumulation, funding, payment, and valuation comparisons when one constant rate and one equal recurring payment describe the scenario. It can help an advisor check a TVM relationship or compare scenarios before discussing the result in context.

Outside this model

Taxes, fees, inflation adjustments, and investment risk.
Irregular cash flows or payments that change by period.
Rates that change over time or separate compounding conversions.
Calendar dates, day-count conventions, and automatic unit conversion.

Inputs and Outputs

Field names and ordering below follow the active interactive calculator configuration. The selected unknown is not entered; the other four TVM variables are required.

Time Value of Money inputs and outputs
Field	Format	Meaning	Interpretation
Solve Forinput	Selection	The one unknown variable the calculator will solve. The selected field is removed from the four known-value inputs.	Available choices are FV, PV, PMT, I/Y, and N.
Payment Timinginput	Selection	Whether each equal recurring payment occurs at the beginning or end of its period.	Payment timing affects the recurring PMT stream, not PV or FV timing.
Number of Periods (N)input	Decimal periods	The total number of equal periods in the model, expressed in the same time unit as the rate and payment.	When supplied, N must be greater than zero.
Rate per Period (I/Y %)input	Percentage per period	The constant interest or growth rate applied during every period.	Enter 7 for 7%. When supplied, I/Y must be greater than −100%.
Present Value (PV)input	Signed amount	The value at the beginning of the modeled series.	Use a positive or negative sign according to whether the value is received or paid from the chosen perspective.
Payment per Period (PMT)input	Signed amount per period	The equal recurring amount paid or received in each period.	Enter zero when the scenario has no recurring payment.
Future Value (FV)input	Signed amount	The value at the end of the modeled series.	Use a sign consistent with the same cash-flow perspective used for PV and PMT.
Solved Valueoutput	Mode-dependent result	The calculated value of the selected unknown, labeled as FV, PV, PMT, I/Y, or N.	Amounts use signed currency formatting; I/Y uses percent formatting; N uses decimal-number formatting.

Field: Solve Forinput
Format: Selection
Meaning: The one unknown variable the calculator will solve. The selected field is removed from the four known-value inputs.
Interpretation: Available choices are FV, PV, PMT, I/Y, and N.

Field: Payment Timinginput
Format: Selection
Meaning: Whether each equal recurring payment occurs at the beginning or end of its period.
Interpretation: Payment timing affects the recurring PMT stream, not PV or FV timing.

Field: Number of Periods (N)input
Format: Decimal periods
Meaning: The total number of equal periods in the model, expressed in the same time unit as the rate and payment.
Interpretation: When supplied, N must be greater than zero.

Field: Rate per Period (I/Y %)input
Format: Percentage per period
Meaning: The constant interest or growth rate applied during every period.
Interpretation: Enter 7 for 7%. When supplied, I/Y must be greater than −100%.

Field: Present Value (PV)input
Format: Signed amount
Meaning: The value at the beginning of the modeled series.
Interpretation: Use a positive or negative sign according to whether the value is received or paid from the chosen perspective.

Field: Payment per Period (PMT)input
Format: Signed amount per period
Meaning: The equal recurring amount paid or received in each period.
Interpretation: Enter zero when the scenario has no recurring payment.

Field: Future Value (FV)input
Format: Signed amount
Meaning: The value at the end of the modeled series.
Interpretation: Use a sign consistent with the same cash-flow perspective used for PV and PMT.

Field: Solved Valueoutput
Format: Mode-dependent result
Meaning: The calculated value of the selected unknown, labeled as FV, PV, PMT, I/Y, or N.
Interpretation: Amounts use signed currency formatting; I/Y uses percent formatting; N uses decimal-number formatting.

Methodology

The implementation converts I/Y from a percentage to a decimal rate and represents payment timing as t = 0 for end-of-period payments or t = 1 for beginning-of-period payments. It then solves the signed TVM relationship for the selected unknown.

Traditional signed TVM relationship

0 = FV + PV {(1 + r)}^{N} + PMT \frac{{(1 + r)}^{N} - 1}{r} (1 + r t)

Here r is the decimal rate per period. The final factor shifts the equal PMT stream one period earlier when payments occur at the beginning.

FV, PV, and PMT are solved directly from this relationship. I/Y and N use numerical financial solvers when the non-zero-rate relationship does not have the corresponding direct branch. Some combinations can be indeterminate, have no usable solution, or fail to converge; those cases return a safe calculation error rather than a partial result.

Zero-rate relationship

0 = FV + PV + PMT N

At a zero rate, growth and discount factors disappear. The calculator uses direct zero-rate branches for FV, PV, PMT, and N and recognizes a near-zero residual when solving I/Y.

A supplied N must be positive and a supplied I/Y must be greater than −100%. A solved N must also be positive, and a solved I/Y must be greater than −100%. The final solved value is rounded to two decimal places using half-up rounding; intermediate calculations are not rounded.

Assumptions and Limitations

Assumptions

N, I/Y, and PMT use the same period unit.
The rate is constant and recurring payments are equal.
Payments occur exactly at the selected period boundary.
Cash-flow signs use one consistent perspective.

Limitations

The model is deterministic and does not represent uncertainty.
It does not validate whether the period unit is appropriate.
Sign patterns can produce economically unintuitive results.
Some rate or period combinations have no unique usable solution.

Selected Sources

This calculator does not rely on a selected external source for its core methodology. Review the methodology, assumptions, and limitations above for the model used.