Finance Calculator
Solve a time-value-of-money equation for the unknown: number of periods, annual rate, present value, payment, or future value. Choose how many periods fall in a year and whether payments occur at the end or the beginning of each period.
Finance Calculator tool
About the Finance Calculator
Cash-flow signs matter. Money you receive is positive; money you pay is negative. A loan of $10,000 is +10000 present value. The payment that retires it is negative. Leaving the sign convention mixed is the usual reason a TVM problem has no solution.
This is a five-key finance solver, not a bank product. It does not add points, origination fees, or a 365/360 day-count unless you fold those into the cash flows yourself.
How the Finance Calculator works
With i = annual rate ÷ 100 ÷ periods per year, the balance identity is PV × (1 + i)^N + PMT × annuity + FV = 0. Beginning-of-period payments multiply the annuity by (1 + i). At i = 0 the identity is PV + PMT × N + FV = 0.
PV × (1 + i)^N + PMT × [((1 + i)^N − 1) ÷ i] + FV = 0 (end of period)
Annuity due: multiply the PMT factor by (1 + i)
Example
N = 36, 6% nominal, 12 periods/year, PV = 10000, FV = 0, end of period → PMT = −304.22.
How to Use the Finance Calculator
- Choose which variable to solve.
- Set end or beginning-of-period payments.
- Enter the other four cash-flow fields with consistent signs.
- Choose periods per year (1, 2, 4, 12, or 365).
- Read the unknown and the completed set of N, rate, PV, PMT, and FV.
Finance Calculator Examples
Loan payment
PV 10000, FV 0, N 36, 6% monthly compounding → PMT −304.22.
Savings future value
PV −1000 (you invest), PMT 0, N 12, 12% monthly → FV about 1126.83.
How many periods
PV 10000, PMT −304.22, FV 0, 6% monthly → N near 36.
How to Use a TVM Solver
List the five keys. Put a plus on cash in and a minus on cash out. Leave the unknown at any placeholder — this page ignores that field when it is the solve target.
Worked sign patterns
Keep the signs consistent with the row you mean.
| Story | PV | PMT | FV |
|---|---|---|---|
| Borrow and repay | +loan | −payment | 0 |
| Invest a lump sum | −deposit | 0 | +future |
| Save each period | 0 or −seed | −deposit | +goal |
When there is no solution
If payments are too small to retire a loan, N or the rate may not exist in the real numbers. The calculator then shows an error instead of a fake APR.
Frequently Asked Questions
Why is payment negative?
You are paying cash out to retire a positive loan PV.
What is beginning of period?
An annuity due — rent paid at the start of the month. It grows slightly more than an ordinary annuity.
Can I solve for rate?
Yes. The solver bisects a wide interval. Some cash-flow patterns have no real rate.
Is N always an integer?
When you enter N it must be a whole number. When you solve for N the result can be fractional.
Is this the same as the loan calculator?
For an ordinary monthly loan, solving for PMT matches. The loan calculator hides the sign convention.