Annuity Payment Calculator

PMT = P · r / (1 − (1+r)^(−n)). Payment that fully amortizes a principal over n periods at rate r.

Inputs

Per period (monthly = annual/12).

30-year monthly = 360.

Result

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General calculation reads

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How to use this calculator

  • Enter principal.
  • Enter periodic rate (monthly = annual / 12).
  • Enter number of periods.

About this calculator

The amortization formula gives the constant payment that pays off a principal P over n periods at periodic rate r, mixing principal and interest. Used for mortgages, car loans, fixed annuities, bond coupons. For a $100k mortgage at 6% (0.5% monthly) over 30 years (360 months): payment ≈ $599.55/mo.

Frequently asked

Annual vs monthly rate?+
Always match the period. Monthly payments use monthly rate (annual / 12) and number of months.
How is this different from /finance/loan-calculator?+
Same math, different framing. /finance/loan-calculator is consumer-focused (mortgages, autos); this is for finance students and analysts.
What if rate = 0?+
Equal-installment payment with no interest: PMT = P / n. The calculator handles this.
How does interest decline over the term?+
In the early periods most of each payment is interest; later, more is principal. Amortization schedule shows this.
Annuity-due vs ordinary?+
This calculator computes ordinary annuity (payments at end of period). For payments at beginning (annuity-due), divide PMT by (1+r).

Related calculators

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FV = PV × (1 + r)^n. What today's amount grows to over time.
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NPV = sum of discounted future cash flows minus initial investment. Positive NPV = accept project.
Continuous Compounding Calculator
A = P · e^(rt) — the limit of compound interest as the compounding frequency → ∞.

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