Finance Calculator
A full time-value-of-money solver: solve for PV, FV, rate, term or payment.
Inputs
Choose the variable you want to calculate.
Calculated Value
27,442.51
Unit depends on what you are solving for (currency for PV/FV/PMT, % for rate, periods for N).
Periodic Rate (%)
0.500000%
Total Payments
$12,000.00
Interest Component
$5,442.51
Step by step
Present value
= $10,000.00
Periodic rate
6% ÷ 12
= 0.500000%
Total periods
= 60
Future value
$10,000.00 × (1 + 0.005)^60 + $200.00 × annuity factor
= $27,442.51
How it works
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
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.