Free calculator
TVM calculator (PV, FV, PMT, rate, N)
Solve the classic time value of money setup: PV, FV, a level payment (PMT), a nominal annual rate, and N periods—pick which one is unknown, set payments per year, and end vs beginning of period timing. Math follows the usual lump + annuity identity used by Google Sheets and Excel (PV, FV, PMT, RATE, NPER). This is not an IRR/NPV engine, not uneven cash flows, and not an inflation “purchasing power” calculator—see methodology and FAQ.
When to use this calculator
Fast five-key checks that mirror a financial calculator or a single row of Sheets/Excel—without building a full model.
- Back-solve PMT from PV, FV, rate, and N (loan or savings with a known horizon).
- Find the nominal annual rate implied by PV, FV, PMT, and N when the other variables are pinned.
- Estimate periods to a goal (N) when the payment, rate, and starting/ending balances are fixed.
- Compare end vs beginning of period timing (
TYPE0/1) before you paste the same assumptions intoPMT/FV.
Time value of money here means: a present value grows at a constant periodic rate, with optional equal payments each period, to reach a future value after N periods. We keep payment frequency and compounding per period aligned (one periodic rate i = nominal ÷ m).
The five linked variables
PV, FV, PMT, N, and nominal annual rate (converted to i per period using payments per year). Pick one unknown; the page solves the standard lump + level annuity relationship with ordinary or due payments.
The core identity (intuition)
Think “grow PV to the horizon” plus “accumulate each PMT at the same periodic rate,” with one extra step when payments fall at the start of each period (due). At 0%, growth is linear: FV = PV + PMT × N (with timing details folded into the same rule the tool uses).
What we do not model on purpose
IRR, NPV, uneven cash-flow schedules, continuous compounding, taxes, inflation, fees, and changing rates over time belong in a full model or different tools. For monthly savings with a timeline UI, use the compound interest calculator; for payment stream teaching focused on annuity wording, use the annuity calculator.
Treat every number as illustration—your bank, lease, or tax context may add rules this page skips. For equal-payment teaching with PV/FV/PMT language, see the annuity calculator. For contributions and a balance path, open the compound interest calculator. For uneven inflows and time to recover an outlay (not IRR), use the payback period calculator. For a full loan schedule row-by-row, use the amortization schedule calculator.
Google Sheets & Excel
English US/UK names below. Periodic rate is nominal annual ÷ payments per year; TYPE is 0 end, 1 beginning. Replace cell references with yours.
=PMT(annualRate/paymentsPerYear,n,-pv,fv,type)pv and fv follow Excel sign rules (loans often use positive principal and negative payment outflows). type is 0 or 1.
=FV(annualRate/paymentsPerYear,n,pmt,-pv,type)Use consistent signs with PMT and PV so the function returns the FV you expect.
=RATE(n,pmt,-pv,fv,type,guess)*paymentsPerYearRATE returns a periodic rate; multiply by payments per year for a nominal annual line comparable to this page.
=NPER(annualRate/paymentsPerYear,pmt,-pv,fv,type)May return a fraction when the horizon is not a whole number of periods.
Frequently asked questions
What is time value of money (TVM)?
TVM is the idea that money today and money later are not interchangeable unless you specify an interest rate and timing. This page implements the standard PV + level PMT → FV (or solve any one link) used in finance classes and spreadsheets.
Which five inputs does this TVM calculator use?
PV (present value), FV (future value), PMT (equal payment each period), N (number of periods), and a nominal annual rate we convert to a periodic rate using payments per year. You choose one unknown; the other four must be supplied (when relevant for that mode).
Why are my PV/PMT signs “weird” compared to Excel?
Sheets/Excel use cash-flow direction: money out is often negative and money in positive, depending on convention. This tool accepts your numbers as typed and solves the same algebraic identity—if a result looks flipped, try reversing a sign on PV or PMT to match your workbook story.
What does end vs beginning of period mean?
End (ordinary) puts each payment at the end of the period (Excel TYPE 0). Beginning (due) shifts the payment stream to the start of each period (TYPE 1). That changes accumulation when the rate is non-zero.
How is this different from your annuity calculator?
The annuity page frames equal payments and solves PMT/PV/FV with clear context labels. This TVM page is the combined “five keys” view (adds rate and N solves) for users who think in financial-calculator or spreadsheet terms.
When should I use the compound interest calculator instead?
Use compound interest when you want a timeline, contribution cadence, and compounding choices as a story about growing a balance. This TVM page is a compact solver for PV/FV/PMT/rate/N with equal payments—closer to FV/PMT/RATE/NPER rows.
Is TVM the same as ROI?
No. ROI on our ROI page is a two-number ratio (and optional CAGR) between invested and returned. TVM here handles many periods and a level payment stream with an explicit rate—different question, different formulas.
Can this calculate IRR or NPV?
No. IRR/NPV require a schedule of dated or period-by-period cash flows that may change each period. This page assumes one PV, one FV, and equal PMT across N periods at one rate.
Which Excel or Google Sheets functions match this page?
The usual family is PV, FV, PMT, RATE, and NPER with rate ÷ payments per year, N, and TYPE. The spreadsheet cards show English patterns; in localized Excel use Insert function to match your language pack.
Is this financial, tax, or lending advice?
No. It is a free educational calculator—not a quote, not a suitability recommendation, and not a substitute for qualified professionals when decisions have money on the line.