Finance Calculator
Generic Time Value of Money (TVM) calculator. Solve for the number of periods, interest rate, present value, payment, or future value from the other four.
How It's Calculated
Formula
PV(1+r)^N + PMT\frac{(1+r)^N-1}{r} + FV = 0 \quad (r \neq 0), \qquad PV + PMT \cdot N + FV = 0 \quad (r = 0)The Finance Calculator is a generic Time Value of Money (TVM) solver: it relates five variables — the Number of Periods (N), the periodic Interest Rate (I/Y), the Present Value (PV), the Payment per period (PMT), and the Future Value (FV) — through a single identity. Any four of the five can be supplied, and the calculator solves for the remaining one. This sign convention treats cash you receive as positive and cash you pay out as negative: for a loan, the amount borrowed (PV) is positive and the repayment (PMT) is negative; for a savings plan, the deposits (PMT) are negative and the resulting balance (FV) is positive. N and I/Y are solved with closed-form algebra where possible; when the interest rate itself is the unknown, the calculator reuses the project's shared numerical rate solver rather than an approximate or duplicated method.
Worked Examples
Solve FV: N=10, I/Y=5%, PV=$1,000, PMT=-$100
- Periodic rate r = 5% / 100 = 0.05.
- (1+r)^N = (1.05)^10 = 1.628894626777442.
- FV = -[PV×(1+r)^N + PMT×((1+r)^N - 1)/r]
- FV = -[1000×1.628894626777442 + (-100)×(1.628894626777442-1)/0.05]
- FV = -[1628.89 - 1257.79] = -$371.11.
Solve PMT: N=12, I/Y=1%, PV=$1,000, FV=$0 (loan sign convention: PV positive, PMT negative)
- Periodic rate r = 1% / 100 = 0.01.
- (1+r)^N = (1.01)^12 = 1.126825030131969.
- PMT = -[PV×(1+r)^N + FV] × r / [(1+r)^N - 1]
- PMT = -[1000×1.126825030131969] × 0.01 / 0.126825030131969 = -$88.85.
Solve N (zero-rate case): I/Y=0%, PV=-$1,000, PMT=$100, FV=$0
- At a 0% rate the identity simplifies to PV + PMT×N + FV = 0.
- N = -(PV + FV) / PMT = -(-1000 + 0) / 100 = 10 periods.
Frequently Asked Questions
What do N, I/Y, PV, PMT, and FV mean?
N is the number of periods (payments/compounding intervals). I/Y is the interest rate per period, as a percent. PV is the present (starting) value. PMT is the payment made or received each period. FV is the value at the end of the last period. This is the same five-variable model used by standard financial calculators (HP12C, BA II Plus) and by Excel's PV/FV/PMT/NPER/RATE functions.
What is the sign convention, and why does it matter?
Cash you receive is entered as a positive number; cash you pay out is entered as a negative number. For a loan, the amount you borrow (PV) is positive because you receive it, and your repayments (PMT) are negative because you pay them. For a savings plan, your deposits (PMT) are negative and the resulting balance (FV) is positive. Getting the signs backwards will not produce an error, but it will produce a mathematically different (and likely nonsensical) scenario, since the underlying identity treats all cash flows as netting to zero.
What does 'I/Y' being a rate per period mean — is it an annual rate?
I/Y is the interest rate for one period, not necessarily one year. This calculator is deliberately generic and period-based: if your periods are months, enter the monthly rate; if your periods are years, enter the annual rate. No monthly/annual conversion is applied automatically, since the calculator has no fixed compounding-frequency assumption.
Why can solving for N or I/Y sometimes report 'no real solution'?
The TVM identity is a specific algebraic relationship; not every combination of the other four values has a real, finite solution for the fifth. Solving for N requires taking a logarithm of a positive ratio — if that ratio is zero or negative, no real number of periods satisfies the equation. Solving for I/Y searches numerically within a wide but bounded interval (from just above -100% to 10,000% per period); if no rate in that range satisfies the equation, or the two supplied cash-flow directions never actually cross, the calculator reports a controlled status rather than a fabricated number.
What happens to the value in the field I'm solving for?
The field you're solving for is hidden while you enter the other four values, and its previous value (if any) is preserved so it reappears if you switch to solving for something else — but it is never read while it is hidden, so any old or invalid value there cannot affect the current calculation.