semkuFinance calculator online
Enter four values to find the fifth. Choose the payment frequency and timing. Money you pay is negative; money you receive is positive.
Year-by-year balance
Rows group the payment periods into years; the last row may cover less than a year. Payments are signed cash flows. Positive interest is earned; negative interest is paid. A negative balance is an amount still owed.
| Year | Regular cash flows | Interest | Balance (FV) at period end |
|---|---|---|---|
| 1 | −$2,400.00 | $683.89 | $13,083.89 |
| 2 | −$2,400.00 | $874.10 | $16,357.99 |
| 3 | −$2,400.00 | $1,076.04 | $19,834.03 |
| 4 | −$2,400.00 | $1,290.43 | $23,524.46 |
| 5 | −$2,400.00 | $1,518.05 | $27,442.51 |
| 6 | −$2,400.00 | $1,759.71 | $31,602.21 |
| 7 | −$2,400.00 | $2,016.27 | $36,018.48 |
| 8 | −$2,400.00 | $2,288.65 | $40,707.14 |
| 9 | −$2,400.00 | $2,577.84 | $45,684.97 |
| 10 | −$2,400.00 | $2,884.86 | $50,969.84 |
Sources and model basis
Appendix J describes the actuarial method for closed-end credit. It is a reference for periodic cash-flow calculations. This calculator uses the assumptions and rounding rules stated here and does not calculate a legally disclosed APR.
Section 3.2.2.1, equation 3-7 (printed page 29), gives the present value of equal annual costs paid at year end. The five-value equation and other payment frequencies and timings are this calculator’s adaptations. These adaptations do not imply NIST endorsement of this calculator or a financial product. Republished courtesy of the National Institute of Standards and Technology.
Calculation rules
The equation is PV·(1+i)^N + PMT·(1+i·T)·((1+i)^N − 1)/i + FV = 0. At i = 0, it becomes PV + PMT·N + FV = 0. For a positive rate, N = ln(X) ÷ ln(1+i), where X = (PMT·(1+i·T) − FV·i) ÷ (PMT·(1+i·T) + PV·i), when this expression defines a positive period count.
Positive cash flows are money you receive; negative cash flows are money you pay. PV is the cash flow at the start, PMT is the regular cash flow, and FV is the cash flow at the end.
i = I/Y ÷ 100 ÷ P/Y. I/Y is the nominal annual rate. Interest compounds once per payment period, so C/Y = P/Y. This is not an APY calculation or a calculation of a legally disclosed APR.
T = 0 for payments at the end of each period and T = 1 for payments at the beginning. Periods are equally spaced.
Dollar amounts are calculated without intermediate rounding and rounded once to cents. Exact halves round away from zero. Solved rates and period counts are rounded to two decimal places. Rounded results are not reused in later calculations.
The rate search covers 0% through 1,000%. Distinct rates that satisfy the equation are reported together, even if they round to the same displayed rate. If no rate satisfies the equation, no numeric rate is shown.
Regular cash flows total PMT × N and exclude PV and FV. Net interest is PV + PMT × N + FV: positive means interest earned and negative means interest paid. These totals are shown for FV, PV, PMT and I/Y results. Year-by-year tables are shown for FV, PV and PMT results. Each row covers up to P/Y periods. Row interest equals the change in balance plus the signed regular cash flows for that row. The starting balance is −PV. Each cell is rounded separately.
The model assumes a fixed rate and equal regular payments. It excludes taxes, fees, inflation and rate changes. The example rate of 6% is illustrative, not a current market rate.
Frequently asked questions
- Why is an amount negative?
- A negative amount is money you pay; a positive amount is money you receive. For FV, a negative result means a payment remains at the end. It does not by itself indicate a calculation error.
- Why can two rates give the same result?
- Some cash-flow patterns change direction twice and satisfy the equation at two different rates. The calculator searches from 0% to 1,000%. Rates are rounded to two decimal places, so two distinct rates can have the same displayed value.
- Are fees or taxes included?
- No. The calculation assumes a fixed rate and equal regular payments. Taxes, fees, inflation and rate changes are excluded.
- What do the related calculators cover?
- The loan payment calculator covers monthly loan payments. The loan amortization calculator provides a loan payment schedule. The CD calculator covers CD balances and APY.
Privacy on this page
Calculations run in your browser. The values you enter are not sent to the server or saved in browser storage. Reloading the page returns the inputs to their initial state.
To understand how the page is used and to improve the service, this page sends semku’s own usage statistics and automatic error reports. They go only to the dedicated endpoint under semku.com/api/telemetry/v1/. They are not used for advertising or third-party tracking.
The usage statistics include stages of use (such as starting an operation or requesting a copy), the times they occur and fixed identifiers that distinguish the page and feature. They do not include the values you enter, the results shown or the text you copy. Inputs are not sent as hashes or as size categories either. The full URL and search terms are not sent.
Operations and sessions are distinguished by randomly generated identifiers. In the browser, these identifiers exist only in temporary memory and are not written to cookies or browser storage. No identification based on cookies or combined device characteristics is used.
Error reports contain the error type, code and time, and, where available, a registered program-source identifier with line and column numbers. The error message text and stack traces are not sent. Usage statistics and error reports also carry the site identifier, the deployment version and a random record identifier. For access records such as IP addresses, browser signals (User-Agent Client Hints), region and language, see the paragraph below.
The feedback form sends the rating you chose and the text you typed in the free-text field when you press the send button. The form also sends a random ID that distinguishes the submission, along with the page, site, deployment version and type of request. There are no fields for your name, email address or phone number, and the values you enter are not attached automatically. Before sending your text, the widget removes leading and trailing whitespace and, if you selected a rating, adds [+1] or [-1] at the start; it makes no other changes to your text. After receipt, the collector standardizes line endings and removes leading and trailing whitespace. Please do not enter personal data, passwords, authentication keys or payment details.
To improve the service, we record the country and state/province-level region at the time of your visit (an estimate based on the connecting network), which site you came from including the page path, and one display-language setting announced by your browser (for example, en-US). Location is kept to country and region only; no city or precise position is recorded. When you use the service, connection records, including your IP address, are automatically generated and retained to maintain service security and identify abnormal access. Cloudflare is the data processor for this site. Collection of this item is enabled only after this notice is published; we do not collect it retrospectively for use before collection is enabled. Query strings such as search terms are not recorded, and neither is the full list of preferred languages or the raw request headers. Collection of this information is currently disabled and will only be enabled after this notice is published. If we enable collection, we will collect and use signals your browser reports about its type and version, along with an indication of whether automation tools are being used, to identify bots. These browser signals are estimates and do not conclusively identify your browser's type or version or whether automation tools are being used. We do not collect it retrospectively for use before collection is enabled. The raw User-Agent request header is not recorded. These records are per visit only and use no identifier that links one visit to another. Recording starts only with visits after this notice is published and is not applied retroactively to earlier visits. The region and the referring site have been recorded since 2026-09-20; the display language since 2026-09-24. Browser signals are not recorded yet.
Separately, when you visit the site, the hosting provider records your IP address, the time of the request and user-agent information about your browser and device in Cloudflare Pages’ standard access logs.
For details, see the privacy policy.
Calculations run in your browser without sending your calculation inputs or results to the server. See “Privacy on this page” for information about access data.