A full time-value-of-money solver: solve for PV, FV, rate, term or payment.
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.
Core TVM identity
PV × (1+r)^n + PMT × [(1+r)^n − 1] / r = FV
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.
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.
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.
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.