Quick answer
The time-value-of-money equation PV(1 + i)ⁿ + PMT(1 + i·t)((1 + i)ⁿ − 1) ÷ i + FV = 0 solves for any one of N, I/Y, PV, PMT or FV. With PV = −10,000, monthly payments of −100, 6% annual rate and 120 periods, FV is $34,581.90.
Choose what to solve for, then enter the other variables. The calculator returns the missing value. Use this financial calculator to check your own figures.
Related tools: Investment Calculator: Project investment growth from a rate of return you choose. IRR Calculator: Internal rate of return of an investment from its yearly cash flows. CAGR Calculator: Compound annual growth rate between two values.
How to use the Financial Calculator
- Choose solve for: Future value (FV), Present value (PV), Payment (PMT), Number of periods (N) and Annual rate (I/Y).
- Enter periods per year (a whole number, between 1 and 365). It starts at 12.
- Optionally, enter number of periods (N) (0 or more).
- Optionally, enter annual rate (I/Y) (%) (between -50 and 1000).
- Optionally, enter present value (PV).
- Optionally, enter payment (PMT).
- Optionally, enter future value (FV).
- Choose payments: End of period and Start of period.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Solve for | Choose one: Future value (FV); Present value (PV); Payment (PMT); Number of periods (N); Annual rate (I/Y) | Starts at Future value (FV) |
| Periods per year | A whole number | ≥ 1, ≤ 365, starts at 12 |
| Number of periods (N) (optional) | A number | ≥ 0 |
| Annual rate (I/Y) (optional) | A number, in % | ≥ -50, ≤ 1000 |
| Present value (PV) (optional) | A number | — |
| Payment (PMT) (optional) | A number | — |
| Future value (FV) (optional) | A number | — |
| Payments | Choose one: End of period; Start of period | Starts at End of period |
Formula and method
Formula
PV(1 + i)ⁿ + PMT(1 + i·t)((1 + i)ⁿ − 1) ÷ i + FV = 0, i = rate ÷ periods per year, t = 1 for payments at the start
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Cash-flow sign convention: money you pay out is negative and money you receive is positive. Fields for the unknown are ignored.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Solve for = Future value (FV); Periods per year = 12; Number of periods (N) = 120; Annual rate (I/Y) = 6; Present value (PV) = -10000; Payment (PMT) = -100; Future value (FV) = 0; Payments = End of period.
| Result | Value |
|---|---|
| Future value (FV) | 34,581.9 |
Example 2
Inputs: Solve for = Payment (PMT); Periods per year = 12; Number of periods (N) = 360; Annual rate (I/Y) = 6; Present value (PV) = 250000; Payment (PMT) = 0; Future value (FV) = 0; Payments = End of period.
| Result | Value |
|---|---|
| Payment (PMT) | -1,498.88 |
Example 3
Inputs: Solve for = Present value (PV); Periods per year = 12; Number of periods (N) = 60; Annual rate (I/Y) = 5; Present value (PV) = 0; Payment (PMT) = -300; Future value (FV) = 0; Payments = End of period.
| Result | Value |
|---|---|
| Present value (PV) | 15,897.21 |
The first line is the headline result (future value (FV)). IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Signs matter
Use opposite signs for money in and out: deposits are negative and the future value is positive. Here $10,000 grows to $18,193.97 and the $100 deposits add $16,387.93, for $34,581.90.
Solving for the rate
The rate is solved numerically by bisection between −50% and a high limit, so it needs inputs that have a solution. The payment timing flag t is 1 for payments at the start of each period.
How the result changes with periods per year
Holding every other input at the first worked example, this table changes only periods per year. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Periods per year | Future value (FV) |
|---|---|
| 6 | 56,007.74 |
| 12 | 34,581.9 |
| 24 | 27,467.68 |
| 48 | 24,555.29 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number of periods (N): entering "0" shows "Enter the number of periods." beside that field and no result.
- Periods per year: entering "0" shows "Periods per year must be at least 1." beside that field and no result.
Choosing between the Financial Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [IRR Calculator](/finance/irr-calculator/) | initial investment and cash flows | IRR |
| [CAGR Calculator](/finance/cagr-calculator/) | beginning value, ending value and years | CAGR |
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
| [Mutual Fund Calculator](/finance/mutual-fund-calculator/) | initial investment, monthly contribution and expected annual return | Value after fees |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- Use opposite signs for money in and money out
- Rate solves by bisection between −50% and 500% per period
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number of periods (N) and periods per year to confirm this.
Frequently asked questions
What does N mean?
The number of periods.
What is I/Y?
The annual interest rate.
Can I use it for a loan?
Yes, set PV to the loan and FV to zero.
What does the Financial Calculator calculate?
Time-value-of-money solver for N, rate, present value, payment or future value. It returns Future value (FV).
What formula does the Financial Calculator use?
PV(1 + i)ⁿ + PMT(1 + i·t)((1 + i)ⁿ − 1) ÷ i + FV = 0, i = rate ÷ periods per year, t = 1 for payments at the start. Cash-flow sign convention: money you pay out is negative and money you receive is positive.
What do I need to enter in the financial Calculator?
You enter Solve for, Periods per year and Payments. Optional: Number of periods (N), Annual rate (I/Y) (%), Present value (PV), Payment (PMT) and Future value (FV).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Use opposite signs for money in and money out.
What are the limits of this calculator?
Use opposite signs for money in and money out. Rate solves by bisection between −50% and 500% per period.
What does the “Solve for” option change?
It sets how the financial is worked out. The choices are Future value (FV), Present value (PV), Payment (PMT), Number of periods (N) and Annual rate (I/Y).
What is an example of a financial result?
With solve for Future value (FV), periods per year 12, number of periods (N) 120, annual rate (I/Y) 6 and present value (PV) -10000, the future value (FV) is 34,581.9.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Use opposite signs for money in and money out.
Related calculators
- Investment Calculator — Project investment growth from a rate of return you choose.
- IRR Calculator — Internal rate of return of an investment from its yearly cash flows.
- CAGR Calculator — Compound annual growth rate between two values.
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Mutual Fund Calculator — Growth of a fund investment after its expense ratio.
- Net Present Value Calculator — NPV of an initial outlay and a series of yearly cash flows.
- Asset Allocation Calculator — Dollar amounts for a stock, bond and cash split.
- Capital Gains Calculator — Gain on a sale and tax at the rate you enter.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.