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Calculate Future Value (FV), Periodic Payment (PMT), Interest Rate (I/Y), Number of Periods (N), or Present Value (PV) for constant-rate, equal-payment scenarios. Amounts use USD; rates are assumptions.
Results
Schedule
10 periods| Period | Opening balance | PMT | Interest | Closing balance |
|---|---|---|---|---|
| 1 | $20,000.00 | $-2,000.00 | $1,200.00 | $19,200.00 |
| 2 | $19,200.00 | $-2,000.00 | $1,152.00 | $18,352.00 |
| 3 | $18,352.00 | $-2,000.00 | $1,101.12 | $17,453.12 |
| 4 | $17,453.12 | $-2,000.00 | $1,047.19 | $16,500.31 |
| 5 | $16,500.31 | $-2,000.00 | $990.02 | $15,490.33 |
| 6 | $15,490.33 | $-2,000.00 | $929.42 | $14,419.75 |
| 7 | $14,419.75 | $-2,000.00 | $865.18 | $13,284.93 |
| 8 | $13,284.93 | $-2,000.00 | $797.10 | $12,082.03 |
| 9 | $12,082.03 | $-2,000.00 | $724.92 | $10,806.95 |
| 10 | $10,806.95 | $-2,000.00 | $648.42 | $9,455.36 |
One equation, five unknowns
Choose the variable to solve, then fill the four known fields. Use one cash-flow viewpoint throughout: money received is positive and money paid is negative. For a loan, PV is positive and repayments are negative. For savings, enter the initial deposit and contributions as negative, with the target withdrawal as positive.
I/Y is a nominal annual percentage. With C compounding periods and P payments per year, the payment-period rate is i = (1 + I/Y ÷ 100 ÷ C)^(C/P) − 1. N counts payments, not years: 30 years of monthly payments means N = 360 and P = 12.
The equation is PV(1+i)^N + PMT[(1+i)^N−1]/i × (1+i×t) + FV = 0, where t is 0 for end payments and 1 for beginning payments. At zero interest it becomes PV + PMT×N + FV = 0.
Check a simple example
For an illustrative $10,000 loan at 0% with 10 end-of-period payments and FV = 0, PMT is −$1,000. For a single $10,000 savings deposit, set PV = −10,000 and PMT = 0. At 5% annually for 10 years, FV is approximately $16,288.95.
Why the schedule ends at the opposite of FV
The schedule starts at PV and applies interest and signed payments. Its closing balance is the amount before the terminal cash flow; FV is the offsetting cash flow that closes that balance. In the default example, a positive closing balance corresponds to a negative FV. Signed schedule interest follows the same balance convention and is not an investment performance measure.
What this solver can establish
Known N must be a whole number from 1 to 1,200. A solved N may be fractional; in that case the calculator shows the algebraic answer without rounding up and inventing a final payment. Select a whole N and solve PMT to create an equal-payment schedule.
Rate solving requires exactly one sign change in the combined dated cash flows. Other patterns can have multiple or no rates, so the calculator reports a limit instead of selecting an arbitrary answer. Extreme inputs outside the numeric range are rejected. Negative rates are supported only when each compounding growth factor remains positive.
This model excludes taxes, fees, payment-date irregularities, changing rates and missed payments. It does not reproduce a lender’s legally required APR or establish that a target return is achievable. The schedule uses unrounded internal amounts; a contract that rounds each payment or interest charge can differ.
Formula references checked October 21, 2026: Texas Instruments TVM formulas and Microsoft NPER documentation.
Frequently Asked Questions
Why is FV opposite to the closing balance?
FV is a terminal cash flow. The schedule closing balance is the amount immediately before that offsetting cash flow. Keep inflows positive and outflows negative from one viewpoint.
Is I/Y an effective annual rate?
No. It is nominal annual interest using the selected compounding frequency. Payment frequency determines the conversion to a payment-period rate. The two settings can differ.
What changes for beginning payments?
Each payment occurs one period earlier than an end payment. Its balance therefore experiences one additional period of the assumed interest rate.
Why is there no schedule for fractional N?
An algebraic fractional period does not define a final whole payment. The calculator avoids silently rounding up. Choose a whole N and solve PMT if you need a schedule with equal payments.
Why can the rate solver reject my inputs?
It requires exactly one sign change in the dated cash flows and a finite solution in its numeric range. Ambiguous cash flows or extreme values produce an error rather than an unverified rate.
Are these calculations sent to a server?
The TVM calculation runs in this browser and does not call a calculation API or save the input values. The website may separately use analytics. The calculator is free to use.
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