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Present Value of Annuity

PV of an annuity. Free online Present Value of Annuity. Calculate present value of annuity online — fast, accurate, mobile-friendly, no signup needed.

PV of annuity
$47,140.68

Derivation

  1. ├── 01GivenPMT = 500, r = 5, n = 120
  2. ├── 02Formulat × (1-(1+a / 100 / 12)^(-n)) / (a / 100 / 12)
  3. ├── 03Substitutet × (1-(1+a / 100 / 12)^(-120)) / (a / 100 / 12)
  4. └── 04Compute PV of annuity$47,140.68
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§01What is

Understanding the Present Value of Annuity

The Present Value of Annuity computes PV of annuity from 3 inputs: payment ($), rate (%), periods. PV of an annuity.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Present Value of Annuity sits in that toolkit — it PV of an annuity. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t × (1-(1+a / 100 / 12)^(-n)) / (a / 100 / 12)

Where

PMT
Payment ($)
r
Rate (%)
n
Periods
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Payment ($) = 500, Rate (%) = 5, Periods = 120.

  1. 01Start by noting the input — Payment ($): 500.
  2. 02Start by noting the input — Rate (%): 5.
  3. 03Start by noting the input — Periods: 120.
  4. 04Substitute these values into the formula: t × (1-(1+a / 100 / 12)^(-n)) / (a / 100 / 12)
  5. 05Compute PV of annuity: the calculator returns 47140.7.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Present Value of Annuity Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Payment ($) halved

PMT = 250 (from 500)

Keep every other input at its default and halve the payment ($). See how pv of annuity responds.

  1. 01New Payment ($): 250
  2. 02Baseline PV of annuity: 47140.7
  3. 03New PV of annuity: 23570.3
  4. 04PV of annuity decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Payment ($) doubled

PMT = 1000 (from 500)

Keep every other input at its default and double the payment ($). See how pv of annuity responds.

  1. 01New Payment ($): 1000
  2. 02Baseline PV of annuity: 47140.7
  3. 03New PV of annuity: 94281.4
  4. 04PV of annuity increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Rate (%) halved

r = 2.5 (from 5)

Keep every other input at its default and halve the rate (%). See how pv of annuity responds.

  1. 01New Rate (%): 2.5
  2. 02Baseline PV of annuity: 47140.7
  3. 03New PV of annuity: 53039.2
  4. 04PV of annuity increases by 12.5% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Rate (%) doubled

r = 10 (from 5)

Keep every other input at its default and double the rate (%). See how pv of annuity responds.

  1. 01New Rate (%): 10
  2. 02Baseline PV of annuity: 47140.7
  3. 03New PV of annuity: 37835.6
  4. 04PV of annuity decreases by 19.7% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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