Finance Calculator
A full time-value-of-money solver: solve for PV, FV, rate, term or payment.
About Finance Calculator
Time Value of Money captures the idea that a dollar today is worth more than a dollar tomorrow. The five TVM variables — Present Value, Future Value, Payment, Rate and Number of Periods — are linked by one equation. Given any four, this calculator solves for the fifth. Rate is found iteratively using Newton-Raphson since no algebraic closed form exists.
Formula
Core TVM identity
PV × (1+r)^n + PMT × [(1+r)^n − 1] / r = FV
- PV
- Present value
- FV
- Future value
- PMT
- Payment per period
- r
- Periodic interest rate
- n
- Number of periods
Worked example
With the default values below, Finance Calculator returns Calculated Value of 27,442.51. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Solve forone of Future Value (FV), Present Value (PV), Interest Rate, Number of Periods (N), Payment (PMT)
- Future Value (FV)
- Present Value (PV)minimum 0 $
- 10,000 $
- Future Value (FV)minimum 0 $
- 20,000 $
- Payment per Period (PMT)minimum 0 $
- 200 $
- Annual Interest Rate (%)accepts 0–100
- 6
- Compounding / Payments per Yearaccepts 1–365
- 12
- Number of Periods (N)minimum 1
- 60
- Payment Timingone of End of period (ordinary annuity), Start of period (annuity due)
- End of period (ordinary annuity)
Results
- Calculated ValueUnit depends on what you are solving for (currency for PV/FV/PMT, % for rate, periods for N).
- 27,442.51
- Periodic Rate (%)
- 0.500000%
- Total Payments
- $12,000.00
- Interest Component
- $5,442.51
Step by step
- 1Present value= $10,000.00
- 2Periodic rate= 0.500000%
- 3Total periods= 60
- 4Future value= $27,442.51
Assumptions and limits
- The result is derived only from the 8 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
- This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the 'number of periods' — months or years?
Periods are defined by your Compounding/Payments per Year setting. If that is 12 (monthly), enter 60 for 5 years. If annual (1), enter 5. The calculator converts the annual rate to a periodic rate automatically.
Why can't the calculator solve for rate when PV is zero?
When PV is zero, the equation degenerates: you're asking at what rate does nothing grow to something via payments alone. The system of equations has infinitely many solutions, so a meaningful unique answer doesn't exist.
When would I solve for N (number of periods)?
Classic use-case: given a credit card balance ($5,000 at 18% APR), and you want to pay $200/month — how many months until it's paid off? N gives you that answer directly.
What is the difference between ordinary annuity and annuity due?
Ordinary annuity payments occur at the end of each period (most loans and bonds). Annuity-due payments occur at the start (some leases, insurance premiums). Annuity-due results in slightly higher values because each payment earns one extra period of interest.