Solve any one of the five core time-value-of-money variables: future value, payment, annual interest rate, number of periods, or present value.
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Finance Calculator Results
Review the solved TVM value, rates, cash flows, and period-by-period schedule.
Cash Flow Comparison
Calculation Details
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Period Schedule
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Five-key finance calculator
This calculator solves the five core time-value-of-money variables used by common financial calculators: number of periods (N), annual interest rate (I/Y), present value (PV), periodic payment (PMT), and future value (FV). Select the value to calculate, enter the other four, and choose the payment and compounding settings.
Cash-flow sign convention
Money moving in opposite directions must use opposite signs. If you receive $20,000 today, enter PV as positive. If you then pay $2,000 each period, enter PMT as negative. The calculated FV uses the opposite sign of the ending account or loan balance. A sign error is the most common reason a finance calculator cannot find a meaningful result.
Time value of money formula
The calculator converts the nominal annual rate to an effective rate for each payment period, then solves the standard annuity equation. For end-of-period payments, type is 0. For beginning-of-period payments, type is 1.
PV(1 + r)^N + PMT(1 + r x type)((1 + r)^N - 1) / r + FV = 0
Payment frequency and compounding frequency
P/Y is the number of payments per year and C/Y is the number of times interest compounds per year. When they differ, the periodic rate is converted so each payment period receives the equivalent compounded return. For a typical monthly loan, use 12 for both P/Y and C/Y.
Beginning versus end payments
Ordinary annuities make payments at the end of each period. Annuities due make payments at the beginning, giving every payment one additional period of growth or one period less of loan interest. Rent and lease payments are often due at the beginning; many loan payments are modeled at the end.
Worked example
With N = 10, I/Y = 6%, PV = $20,000, PMT = -$2,000, one payment and one compounding period per year, the calculated FV is about -$9,455.36. The sign means the ending value is opposite the original inflow under the selected cash-flow convention.
APR, APY, and assumptions
This tool treats I/Y as a nominal annual interest rate and converts it using the selected C/Y and P/Y values. It does not add lender fees or independently calculate a disclosed APR. The Consumer Financial Protection Bureau explains that APR can include the interest rate plus certain loan charges. For savings growth, the SEC Investor.gov compound interest calculator illustrates how principal, contributions, time, rate, and compounding affect future value.
Frequently asked questions
What do PV and FV mean?
PV is the value at the start of the calculation. FV is the value after N payment periods, expressed using the opposite-side cash-flow sign convention.
Why can there be no interest-rate solution?
The entered cash flows may never balance at a real rate, or they may permit more than one mathematical rate. This calculator reports the first practical real solution it finds and asks you to review signs when no solution is found.
Can N include a partial period?
Yes. The equation can return a decimal number of periods, but the schedule displays complete periods plus a final partial-period estimate.