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Future Value of Annuity

FV of an annuity. Free online Future Value of Annuity. Calculate future value of annuity online — fast, accurate, mobile-friendly, no signup needed.

FV of annuity
$31,056.46

Derivation

  1. ├── 01GivenPMT = 200, r = 5, n = 120
  2. ├── 02Formulat × (((1+a / 100 / 12)^(n)-1) / (a / 100 / 12))
  3. ├── 03Substitutet × (((1+a / 100 / 12)^(120)-1) / (a / 100 / 12))
  4. └── 04Compute FV of annuity$31,056.46
Did you know?

Benjamin Franklin’s will (1790) left £1,000 each to Boston and Philadelphia on 200-year compound-interest terms — the Boston fund reached $5 million in 1990.

§01What is

Understanding the Future Value of Annuity

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

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Future Value of Annuity sits in that toolkit — it FV 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+a / 100 / 12)^(n)-1) / (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 ($) = 200, Rate (%) = 5, Periods = 120.

  1. 01Start by noting the input — Payment ($): 200.
  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+a / 100 / 12)^(n)-1) / (a / 100 / 12))
  5. 05Compute FV of annuity: the calculator returns 31056.5.
  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 Future 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 = 100 (from 200)

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

  1. 01New Payment ($): 100
  2. 02Baseline FV of annuity: 31056.5
  3. 03New FV of annuity: 15528.2
  4. 04FV of annuity decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Payment ($) doubled

PMT = 400 (from 200)

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

  1. 01New Payment ($): 400
  2. 02Baseline FV of annuity: 31056.5
  3. 03New FV of annuity: 62112.9
  4. 04FV 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 fv of annuity responds.

  1. 01New Rate (%): 2.5
  2. 02Baseline FV of annuity: 31056.5
  3. 03New FV of annuity: 27234.4
  4. 04FV of annuity decreases by 12.3% → 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 fv of annuity responds.

  1. 01New Rate (%): 10
  2. 02Baseline FV of annuity: 31056.5
  3. 03New FV of annuity: 40969
  4. 04FV of annuity increases by 31.9% → 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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