Solve for N, I/Y, PV, PMT, or FV — the five core variables behind loans, mortgages, savings, retirement, and leases — with a full cash-flow schedule and one-click PDF/Excel export. Works the same way as the financial calculators used in finance courses worldwide; no affiliation with or endorsement by Texas Instruments.
Positive = inflow (money received) · Negative = outflow (money paid). Example: for a loan, PV is negative (you receive it as a positive in real life, but enter it negative here) and PMT comes out positive when solved — or flip both signs consistently; the math works either way as long as inflows and outflows have opposite signs.
| Period | Beginning Balance | Interest | Payment | Ending Balance |
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The Time Value of Money (TVM) is one of the foundational concepts in finance: a dollar today is worth more than a dollar received in the future, because today's dollar can be invested and start earning a return immediately. This calculator, modeled in the spirit of the financial calculators widely used in finance, accounting, and CFA coursework, lets you solve for any one of five linked variables once you know the other four.
These five are linked by a single equation, where r is the interest rate per payment period (converted from I/Y, P/Y and C/Y), and F is 1 for BGN mode or 0 for END mode:
Give the calculator any four of the five and it solves the fifth — algebraically for PV, FV, PMT, and N, and using a numerical method (Newton-Raphson) for I/Y, since that one can't be isolated algebraically.
Pro Tip
Always double-check your signs before trusting a result. A present value and a payment moving in the same direction (both positive or both negative) usually means you've described an impossible cash flow — the calculator will often return an error, NaN, or a nonsensical number in that case.
END (ordinary annuity): each payment happens at the end of its period. This is the standard for mortgages, auto loans, and most installment loans.
BGN (annuity due): each payment happens at the start of its period — common for rent and most lease agreements. Switching from END to BGN is not universally "better" or "worse" — it depends on which side of the cash flow you're on: for a saver accumulating a future value, BGN produces a larger FV (each contribution earns one extra period of interest), but for a borrower making payments, BGN means paying earlier in each period, which is a less favorable timing for the person making the payment, not a better one. Always check which role you're in before assuming BGN is the "better" mode.
For ordinary monthly payments with monthly compounding, set both to 12. For a Canadian-style mortgage, keep P/Y at 12 (monthly payments) but set C/Y to 2 (semi-annual compounding) — this calculator converts that combination into the correct effective monthly rate automatically.
The single most common source of wrong answers. Outflows (money you pay) and inflows (money you receive) must have opposite signs. If PV and PMT are both positive (or both negative), you've described a cash flow that doesn't make economic sense, and the result will often be nonsensical.
When solving for N, you'll often get a decimal (e.g., 314.7) rather than a clean whole number — that's normal and means the loan or goal doesn't divide evenly into whole periods at that exact payment. Round up if you need a real payoff date.
Solving for I/Y uses a numerical method (since the rate can't be isolated algebraically). For most realistic finance scenarios it converges quickly, but extremely unusual cash flow patterns can occasionally cause it to fail — if that happens, try entering a closer starting rate as I/Y before solving.
This calculator and guide are for general educational purposes only and are not financial advice. This tool is not affiliated with, endorsed by, or sponsored by Texas Instruments or any calculator manufacturer; "BA II Plus" is referenced only as a familiar point of comparison for finance students. Last updated: June 2026.