● PV · FV · Rate · Periods · PMT

Time Value of Money Calculator

Enter any 4 TVM variables — the calculator solves for the 5th: Present Value, Future Value, Rate, Periods, or Payment.

The time value of money is the core concept of finance: a dollar today is worth more than a dollar tomorrow. Use this calculator to solve any TVM problem — find PV, FV, rate, number of periods, or payment amount.

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TVM Calculator

Select what to solve for, enter the other 4 values

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Solve for

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Known values

Present Value (PV)

Future Value (FV)

Interest Rate per period

Number of periods (years)

periods

Payment per period (PMT)

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Solution

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Formula used

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How it's calculated

TVM: the five variables

FV = PV × (1+r)^n + PMT × [(1+r)^n − 1]/r Solve for PV: PV = [FV − PMT×((1+r)^n−1)/r] / (1+r)^n Solve for r: Numerical (Newton-Raphson) Solve for n: n = ln[(FV×r/PMT + 1)] / ln(1+r) — for no PV or numerical solution when PV ≠ 0 Solve for PMT: PMT = [FV − PV×(1+r)^n] × r / [(1+r)^n−1] Conventions: PV is negative (cash outflow today) FV is positive (cash inflow in future) PMT is negative if payments are outflows

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Solving for
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Computed result
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PV (Present Value): The value today of a future sum of money, discounted at the interest rate.
FV (Future Value): The value at a future date of today's money, grown at the interest rate.
Rate (r): The interest rate per period. If periods are years, enter annual rate; monthly periods need monthly rate.
N (periods): The number of time periods (years, months, quarters) over which the calculation applies.
PMT: A regular periodic payment — an annuity. Positive if received, negative if paid.

Disclaimer: TVM calculations assume constant rates and regular payment timing. Real-world cash flows may be irregular — use NPV/IRR analysis for complex scenarios.

Frequently asked questions

What is the time value of money?

The principle that money available today is worth more than the same amount in the future — because today's money can be invested and earn returns. It underlies virtually all financial calculations: loan payments, investment values, retirement planning, and bond pricing.

What is present value?

Present value (PV) is today's value of money to be received in the future, discounted at the interest rate. PV = FV ÷ (1+r)^n. Example: $10,000 in 10 years at 8%/yr is worth PV = $10,000 ÷ 1.08^10 = $4,632 today.

What is an annuity?

An annuity (PMT) is a series of equal payments at regular intervals — like monthly mortgage payments, pension payments, or regular investment contributions. The TVM formula can solve for any annuity variable.