Present Value of Annuity

Time Value of Money
Updated Apr 2026 • Has calculator

The current worth of a series of equal periodic payments, discounted at a required return.

What is PV of Annuity?

The present value of an annuity calculates what a stream of equal, equally-spaced payments is worth today. An ordinary annuity makes payments at the end of each period (bonds, most mortgages). By discounting each future payment back to the present and summing them, PVA tells investors what they should be willing to pay today for that income stream. The formula is widely used to price fixed-income securities, size mortgages, value lease obligations, and determine lump-sum equivalents for structured settlements.

Formula

PVA = PMT × [1 − (1 + r)^−n] ÷ r

Worked Example

Worked example — Fixed Annuity — Insurance Company Illustration

20-year payout, 5% discount rate

Step 1  Annual payment (PMT): $5,000
Step 2  Discount rate: 5.0%
Step 3  Periods: 20 years
Step 4  PVA = $5,000 × [1 − (1.05)^−20] / 0.05 = $5,000 × 12.462 = $62,311
Step 5  → Receiving $5,000/year for 20 years at 5% is equivalent to a lump sum of ~$62,311 today

Source: CFA Institute — Fixed Income & Time Value of Money, 7th ed. (2024-01-01)

Calculate PV of Annuity

Recurring payment amount

Annual discount rate

Total number of payment periods

Present Value of Annuity

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Not investment advice.

How to Interpret PV of Annuity

< 0
Zero or Negative — re-check inputs
> 0
Positive PVA — lump-sum equivalent of the annuity

📚 Time Value of Money — Complete the path

  1. Present Value
  2. Future Value
  3. PV of Annuity
  4. FV of Annuity
  5. Growing Perpetuity
Sources
  1. CFA Institute — Fixed Income & Time Value of Money, 7th ed.
  2. Investopedia — Annuity