Time Value of Money solver — enter any 4 of 5 variables and instantly solve for PV, FV, Rate, N, or PMT.
Leave exactly one field blank — it will be solved for you.
Tip: use negative values for cash outflows (payments you make) and positive for inflows (money you receive).
Solved Variable
PV
—
FV
—
I/Y (Annual)
—
N (Months)
—
PMT (Monthly)
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5 TVM Variables
PV — Present Value
Current worth of a future sum.
FV — Future Value
Value of money at a future date.
I/Y — Interest Rate
Annual rate, divided monthly.
N — Periods
Number of payment periods (months).
PMT — Payment
Regular payment per period.
Sign Convention
Use negative (−) for cash outflows — money you pay out, like loan payments or an investment you make.
Use positive (+) for inflows — money you receive, like a loan disbursement or savings return.
How It Works
The TVM equation links all five financial variables. Solving for rate or N requires numerical methods (Newton–Raphson or logarithms), while PV, FV, and PMT have closed-form algebraic solutions used by financial calculators worldwide.
Formula
About This Tool
This TVM finance calculator solves the standard five-variable Time Value of Money equation used in financial analysis, loan structuring, retirement planning, and investment valuation. It mirrors the logic of the HP-12C and Texas Instruments BA II Plus financial calculators.
Enter any four of the five variables — Present Value, Future Value, interest rate (I/Y), number of periods (N), and payment (PMT) — and the tool will instantly solve for the missing one. Supports both ordinary annuities (end-of-period payments) and annuities due (beginning-of-period payments).
Periods and payments are calculated on a monthly basis. Annual rates are automatically divided by 12 for monthly compounding consistent with most consumer loan and investment scenarios.
Solve for Any Variable
PV, FV, Rate, N, or PMT — leave one blank and the tool finds it.
Both Annuity Types
Ordinary annuity (end) or annuity due (begin) — toggle anytime.
Balance Chart
See your balance evolve month-by-month with a smooth area chart.
Sign Convention
Outflows negative, inflows positive — matches HP-12C convention.
Numerical Solver
Newton–Raphson iteration for Rate; closed-form for PV, FV, PMT.
Live Updates
Solved value highlighted instantly; charts redraw on each calculate.
Solve for any TVM variable in five quick steps.
Decide which of the five TVM variables you want to solve for: PV, FV, Rate, N, or PMT.
Leave the unknown field blank. Enter outflows as negative and inflows as positive (HP-12C convention).
Choose End for ordinary annuities (most loans) or Begin for annuities due (some leases).
The solved value appears highlighted in the results grid along with a balance-over-time chart.
Change one value and recalculate to explore how each variable affects the others.
The Balance tab shows your account value over time; Cash Flows shows the timing and direction of each payment.
Common questions about Time Value of Money calculations.
The Time Value of Money (TVM) is the core principle that a dollar today is worth more than a dollar in the future because it can be invested to earn returns. The five TVM variables (PV, FV, I/Y, N, PMT) describe every fixed-rate financial transaction.
Present Value is the current worth of a future sum or series of cash flows, discounted at a specific rate of return. PV answers: "How much is a future payment worth today?" A lump sum of $10,000 due in 5 years at a 5% discount rate has a PV of about $7,835 today.
Cash outflows (money you pay out, e.g. loan payments) are negative. Cash inflows (money you receive, e.g. a loan disbursement or investment return) are positive. This matches the HP-12C and BA II Plus conventions.
An ordinary annuity pays at the end of each period (most mortgages and loans). An annuity due pays at the beginning (some leases and insurance premiums). Annuity due values are exactly (1 + r) times the ordinary annuity value.
PV, FV, and PMT have direct algebraic solutions. However, solving for Rate (I/Y) requires numerical iteration (Newton–Raphson) because the equation cannot be inverted analytically. Solving for N uses a logarithm when PMT is non-zero. Both methods converge quickly to high precision.