Present Value of Annuity Calculator

An annuity is a series of equal payments — a pension, a lease, lottery installments. Its present value is what that whole stream is worth as a single amount today. Enter the payment, the rate per period and the number of periods, and choose whether payments land at the start or end of each period.

Results

Formula

Each payment is discounted for the time until it arrives, and the geometric series collapses into one formula:
PV = Payment × (1 − (1 + r)−n) ÷ r
Annuity due multiplies the result by (1 + r) because every payment arrives one period sooner.

How to use this calculator

  1. Enter the payment amount and the interest rate per period (match the period to the payment — monthly payments need a monthly rate).
  2. Enter the number of payments.
  3. Choose end-of-period or start-of-period timing, then Calculate.
Present Value of Annuity Calculator — how the calculation works, illustrated$
Present Value of Annuity Calculator — how the calculation works, illustrated

Worked example

$1,000 a year for 10 years at 5%, payments at each year-end.

  1. Annuity factor: (1 − 1.05⁻¹⁰) ÷ 0.05 ≈ 7.7217.
  2. PV: 1,000 × 7.7217 ≈ $7,721.73.

Result: The stream is worth about $7,721.73 today — less than its $10,000 total, because later payments are discounted.

Frequently asked questions

Ordinary annuity vs annuity due — which is more common?

Ordinary annuities (end of period) cover most loans and bonds. Annuity due (start of period) fits rent and many leases, where payment is due up front — and it is always worth slightly more.

How does this value a pension or lottery?

A pension is a life annuity (payments for an uncertain number of periods — actuaries use life expectancy). A lottery annuity has fixed periods, so this formula applies directly at an appropriate discount rate.

What if the rate is zero?

Then no discounting happens and the present value is simply payment × periods — the calculator handles that case.

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