Finance Calculator

Before you calculate

Use this calculator when you need one generic TVM variable from the others and the cash-flow signs, period count, payment frequency, compounding frequency, and payment timing are explicit. Use Present Value or Future Value for narrower discounting or accumulation questions, Payment, Loan Payment, Interest Rate, APR, or Amortization for borrowing workflows, and official CFPB, Regulation Z, lender, Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product, adviser, legal, or local regulator sources for APR, lending disclosure, annuity, retirement-income, tax, investment-product, legal, product-specific, or jurisdiction-specific questions.

Formula summary

The app converts annual I/Y into a per-payment rate with r = (1 + interestRate / 100 / compoundPeriodsPerYear)^(compoundPeriodsPerYear / paymentPeriodsPerYear) - 1. The timing factor is 1 for end-of-period PMT and 1 + r for beginning-of-period PMT. Future value uses FV = -(PV * (1 + r)^N + PMT * (((1 + r)^N - 1) / r) * timingFactor), with FV = -(PV + PMT * N) when r is 0. Periodic payment and present value are rearrangements of the same equation. Interest-rate solve uses bisection over annual rates from -99.999% to 1000%, period-count solve uses bisection from 0 to 12000 periods, sumPeriodicPayments equals PMT * N, and totalInterest is abs(FV + PV + sumPeriodicPayments).

Worked example

Example: five TVM solve modes from fixture-backed inputs

Default FV solve: N = 10, I/Y = 6%, PV = $20,000, PMT = -$2,000, P/Y = 1, C/Y = 1, and end-of-period payments produce FV = $-9,455.36, sum of periodic payments of $-20,000.00, and total interest of $9,455.36. PMT solve with the same N, I/Y, PV, P/Y, C/Y, timing, and FV = $0 returns PMT = $-2,717.36, sum of payments of $-27,173.59, and total interest of $7,173.59. PV solve with N = 2, I/Y = 10%, PMT = $0, and FV = $-121 returns PV = $100.00 and total interest of $21.00. Changing the default FV example to beginning-period PMT changes the timing factor to 1.06 and returns FV = $-7,873.67. Using PMT = $-2,717.36 and FV = $0 over 10 periods returns I/Y = 6.00%, while solving N with that payment and rate returns 10 periods.

The examples show the TVM equation, signs, payment timing, and solver branches. They are not APR disclosures, lender quotes, annuity illustrations, retirement-income promises, tax calculations, investment recommendations, product comparisons, legal answers, or personal finance advice.

Assumptions

• The calculator follows a cash-flow sign convention: money moving in one direction and money moving in the opposite direction should usually have opposite signs. A sign mistake can still produce a mathematical result that does not match the intended scenario.
• N is a period count, not automatically a number of years. Payments per year, compounding times per year, annual I/Y, and beginning or end PMT timing must describe the same schedule for the result to be meaningful.
• Scoped independent comparator checks pass 4 of 4 scoped fixtures for future value, periodic payment, present value, and beginning-period future value. Interest-rate and period-count solves are covered by deterministic source tests and app-output checks, but not by the current independent comparator replay slice. CFPB APR guidance and Regulation Z sections 1026.18 and 1026.22 are needed before APR, amount-financed, finance-charge, payment-schedule, total-of-payments, disclosure, lender, or legal lending claims. Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product documents, lender disclosures, annuity contract materials, and local regulators are needed before investment-product, annuity, retirement-income, tax, insurance, legal, product-specific, regulated-advice, or jurisdiction-specific claims. Results are educational estimates, not financial, tax, legal, lending, investment, retirement, insurance, regulated-product, consumer-rights, or personalised advice.

Common mistakes to avoid

• Entering PV, PMT, and FV with the same sign when the scenario needs opposite cash-flow directions. The calculator does not infer whether a value is a deposit, withdrawal, loan advance, or repayment.
• Mixing annual rates with monthly payments while leaving P/Y or C/Y at annual settings. Change the payment and compounding frequency fields before comparing monthly, quarterly, or annual schedules.
• Treating totalInterest as a lender finance charge, APR disclosure, account statement, annuity quote, tax result, retirement-income guarantee, investment recommendation, product comparison, or legal answer. It is only the app's mechanical balancing amount from the entered TVM cash flows.

Methodology and sources

This calculator is an original implementation based on documented formulas, app-specific assumptions, deterministic fixtures, edge cases, rounding policy tests, and internal validation. It is not copied from a single source.

Outputs are checked with deterministic fixtures, edge cases, rounding policy tests, and internal independent comparator checks where overlapping outputs are available. The result remains an educational estimate, not a quote, approval, tax answer, or personalised advice.

Formula version 2026.05.21-generic-tvm-five-key. The version marks the calculation logic and validation fixture set used for this estimate.

• CFPB APR versus interest-rate guidance should be used when copy explains how generic TVM interest-rate solves differ from APR, finance charges, lender pricing, or broader borrowing-cost claims.
• CFPB Regulation Z sections 1026.18 and 1026.22 should be used when copy discusses amount financed, payment schedule, total of payments, finance charge, APR determination, disclosure tolerances, or Truth in Lending terminology.
• Investor.gov, FINRA, SEC, IRS, FCA, MoneyHelper, product documents, lender disclosures, and relevant local regulators should be used before copy frames generic TVM math as annuity contract values, retirement-income guarantees, tax treatment, regulated investment products, lender quotes, product availability, legal claims, or jurisdiction-specific guidance.

Estimate only

The result is educational and is not financial, tax, legal, lending, investment, or regulated advice. Real provider terms, fees, rates, taxes, and personal circumstances can change the final answer.

Formula and help: read the full finance calculator methodology notes.

Related reading

• How Calcs.finance validates calculator formulas
• Estimate limitations and not-advice disclaimer

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