Annuity Calculator

Solve FV, PV, Payment, or Periods. Supports ordinary annuity vs annuity due, plus compounding/payment frequency.

How to Use

  1. Pick what you want to solve for (FV, PV, Payment, or Periods).
  2. Enter the other values (rate, frequencies, and any required inputs).
  3. Choose Ordinary (end of period) or Due (beginning of period).
  4. Open “Show Work” to see the formula and substituted steps.
Result Overview
Instant output + sanity checks (no API required).
Periodic Rate
—
Payments / Yr
—
Comp / Yr
—
Timing
—
Notes
  • Ordinary = deposits at end of each period.
  • Due = deposits at beginning (typically multiplies by (1+i)).
  • Frequency mismatch uses an effective-per-payment rate.
Inputs & Settings
Pick a solve target, fill required fields, get instant results.
Choose the unknown. Enter the rest below.
Payment each period (usually monthly).
APR input; periodic rate is derived from frequency settings.
Starting amount (optional for some solve modes).
Target amount (optional for some solve modes).
Used with Payments/Year to compute total periods N.
If you fill this, years can be optional (depends on solve mode).
Sets payment period length for N and periodic rate.
Used to derive effective rate per payment if different from payment frequency.
Show Work (step-by-step)
—
Work is shown using the periodic rate per payment (i) and periods (N).

Formulas

These are the standard annuity equations using periodic rate i and periods N.

  • FV (ordinary): FV = PV(1+i)^N + PMT * (( (1+i)^N - 1 ) / i)
  • PV (ordinary): PV = FV/(1+i)^N - PMT * (( (1+i)^N - 1 ) / (i(1+i)^N))
  • PMT (ordinary): PMT = (FV - PV(1+i)^N) * i / ((1+i)^N - 1)
  • Due adjustment: multiply the payment term by (1+i)
If compounding frequency differs from payment frequency, the tool uses an effective rate per payment.

FAQ

Ordinary annuity vs annuity due?

Ordinary annuity assumes payments happen at the end of each period. Annuity due assumes payments happen at the beginning, so each payment earns one extra period of interest.

What if I enter both Years and N?

The calculator can prefer N (total periods) for precision. If you enter Years, it will compute N = Years × Payments/Year. (Your JS will define the exact precedence.)

Does this include taxes, fees, inflation?

No—this is a clean time-value-of-money model. Use after-tax or inflation-adjusted rates if needed.

Tool Info

Last updated:

Updates may include solver improvements, added frequency options, and edge-case handling.