Why are some values negative?

Financial calculators use a cash-flow sign convention: money you receive is positive, money you pay out is negative. PV, PMT and FV describe the same stream from one side, so they can't all carry the same sign — if you invest PV out of your pocket and receive FV back, one of them is negative. The calculator enforces the standard identity PV(1+i)^N + PMT·s + FV = 0, exactly like a BA II Plus.

What are P/Y and C/Y?

P/Y is how many payments you make per year; C/Y is how many times interest compounds per year. They are often equal (12 and 12 for a monthly loan) but not always — a Canadian mortgage compounds semiannually (C/Y = 2) while payments are monthly (P/Y = 12). The calculator converts the annual rate I/Y into the true per-payment-period rate using both settings.

Why can't it solve for I/Y?

A rate exists only when the cash flows change sign — money goes out and money comes back. If PV, PMT and FV all pull the same direction, no interest rate balances the equation, and physical calculators throw the same Error 5. Check your signs: typically an investment is PV negative (out), contributions negative or zero, and FV positive (back in).

What does 'PMT at the beginning' change?

It switches from an ordinary annuity (payment at period end) to an annuity due (payment at period start, like rent or a lease). Each payment then earns one extra period of interest, which changes every solved value — the setting matters more than most people expect.

Finance Calculator

The five time-value-of-money keys, like a BA II Plus or HP 12C. Click the key you want solved — enter the other four, with signs: money in is +, money out is −.

N (# of periods)

I/Y (Interest per year)

PV (Present Value)

PMT (Periodic Payment)

FV (Future Value)

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The Time Value of Money, in Five Keys

Imagine someone owes you $500. Take it all today, or in four installments spread over a year? Almost everyone takes it today — not from impatience, but because money in hand can be put to work immediately: spent, invested to earn interest, or used to retire debt that is charging interest. That gap between a dollar today and a dollar promised later is the time value of money, and it is why banks pay you (a little) for deposits and charge you (more) for loans: interest is the price of having money at hand. Five variables describe nearly every such problem:

N — the number of periods (months, years — whatever P/Y defines).

I/Y — the nominal interest rate per year, before the P/Y and C/Y settings convert it to a per-period rate.

PV — present value: what a future stream is worth today, or what you start with.

PMT — a payment of the same amount every period: rent received, a mortgage paid, a deposit made.

FV — future value: the balance at the end, after growth and payments.

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The $100 example every textbook starts with

Put $100 (PV) in an account paying 10% (I/Y) a year. After one year you have $100 × 1.10 = $110 (FV): each dollar grew to 1 + 0.10 = $1.10. Leave it a second year and the $110 earns $11, giving $121 — and that $121 has four parts: the original $100, the first year's $10 of interest, the second year's $10 on the principal, and $1 of interest on the first year's interest ($10 × 10%). That last dollar is compounding, and over long horizons it quietly becomes the biggest part. Run it backwards and you get PV: $121 arriving in two years, discounted at 10%, is worth exactly $100 today. Discounting is just interest with the clock reversed.

Mind the signs — the one thing everyone gets wrong once

Physical financial calculators insist on a cash-flow sign convention: money received is positive, money paid out is negative. The five keys obey one identity — PV(1+i)^N + PMT·s + FV = 0 — so at least one of PV, PMT, FV must be negative for a rate to exist. Saving toward a goal? Your starting balance and deposits are outflows (−), the target FV is an inflow (+). Borrowing? The loan lands in your account (+PV), payments leave (−PMT), and FV is usually 0. Get the direction right and the "wrong sign" answer everyone complains about disappears.

PMT: the payment questions

PMT turns this from a textbook exercise into the questions people actually ask. A rental property paying $1,000 a month for 10 years — what is that stream worth today (solve PV)? A business throwing off $100 a year forever-ish — what would you pay for it? A $30,000 down payment plus $1,000 a month — what house does that buy, and what does it truly cost? The formulas are fiddly enough that they belong in a calculator; just remember the timing setting. Rent and leases are paid at the beginning of each period (annuity due), loans at the end — and the difference compounds into real money.

Why this little calculator runs the whole site

Business students are rarely allowed into a finance exam without a BA II Plus or HP 12C, because the profession runs on these five keys: every mortgage, loan, lease, and bond price is a TVM problem wearing a costume. This page is that calculator with two things the plastic version lacks — a graph of how the values move, and the full period-by-period schedule. Under the hood, most of CalcNova is this same engine specialized: the investment calculator is this math in friendlier clothes (starting amount and contributions instead of PV and PMT signs), and the financial calculators list is largely a catalog of TVM questions, each with its own form. Learn these five keys and you have learned the site.

FAQ

Why the negative numbers?

Sign convention: in is +, out is −. PV, PMT and FV view the same stream from one side, so they can't all be positive — see the signs section above.

When do P/Y and C/Y differ?

Canadian mortgages are the classic case: interest compounds twice a year (C/Y = 2) but payments are monthly (P/Y = 12). Most U.S. loans are 12 and 12.

I/Y won't solve — what's wrong?

No sign change, no rate. If money only flows one way, no interest rate balances the identity — physical calculators throw Error 5 for the same reason.

Beginning or end of period?

Rent, leases and insurance: beginning (due immediately). Loans and most savings plans: end. Each beginning-mode payment earns one extra period of interest.

Disclaimer: This calculator provides estimates for educational purposes only and does not constitute financial advice. Rates are assumed constant over the full term.