Time value of money.
Find the present value, the payment, the future value, the number of payments or the interest rate of a series of equal payments. It explains the arithmetic; it does not tell you what to do.
This calculator is general information, not individualized tax, legal, or financial advice. It does not account for any particular situation, and it is not a substitute for advice from a professional who knows yours.
Looking for a loan with a payment schedule? Use the loan calculator.
Your numbers
Example figures are filled in. Change any of them.
Money you receive is positive and money you pay is negative, all from one point of view. Borrowing $250,000 and repaying it: the loan is +250,000 and each payment is negative. Saving $200 a month: each deposit is −200 and the balance you end with is positive.
What it is worth now. Negative if you pay it.
What is left or owed after the last payment. 0 for none.
A whole number, up to 100 years of payments.
−50% to 1,000%. 0 and negative rates are allowed. Up to four decimals.
That rate is 6.6972% effective annual, and 0.5417% per payment period.
Optional. nominal, effective annual, per payment period
Enter a rate in any of the three forms to see the other two. The rates shown are mathematical conversions, not substitutes for legally required APR or APY disclosures.
Up to four decimals.
| Form | Rate |
|---|---|
| Nominal annual rate | 6% |
| Effective annual rate | 6.1678% |
| Rate per payment period | 0.5% |
Each is shown to as many decimals, up to four, as the calculation can be sure of.
Result
- The calculator solves one equation: the value now, plus each payment grown to the end, plus the value later, add up to zero. Money received counts as positive and money paid as negative.
- Each payment period grows by a factor of (1 + the nominal annual rate ÷ compounding periods per year) raised to the power compounding periods ÷ payments per year. That is how the compounding and payment frequencies are kept independent of each other.
- Amounts are worked out in exact arithmetic and rounded to the nearest cent, halves away from zero. A figure is shown only when the calculator can show that the cent is right.
- The number of payments is a whole number. When the answer is not whole, you are shown the fractional answer and what the value would be after the whole payments on either side of it.
- Some problems have two interest rates that work, or one that just touches zero, or none. The calculator finds every rate from −50% to +1,000% (nominal, for the compounding chosen) and shows them all. It never picks one for you.
- If the calculator cannot decide an answer, it says so and why. That is different from "there is no answer", which it says only when it can prove it.
- Everything is calculated in your browser. Nothing you enter is sent, stored or put in the address of the page.
Amounts up to $1,000,000,000 in; results up to $1,000,000,000,000. Payments up to 100 years, at 1, 2, 4, 12, 24, 26 or 52 a year. Nominal rates from −50% to +1,000%. Fees, taxes, variable rates and uneven payments are not modeled. The interest rates this calculator shows are mathematical conversions, not substitutes for legally required APR or APY disclosures.