Future Value of an Annuity: Definition, Example, Interpretation

When businesses or individuals make regular, equal payments into an investment or savings vehicle, they often want to understand how much that stream of payments will be worth in the future.

This accumulated amount is called the future value of an annuity, and it’s a core concept in both financial planning and corporate finance.

Understanding how to calculate it helps in budgeting for long-term goals, evaluating retirement plans, and assessing investment opportunities with periodic contributions.

What is the Future Value of an Annuity?

An annuity is a series of equal payments made at regular intervals—monthly, quarterly, or annually. The future value of an annuity is the total value of all payments plus the interest they earn over time.

The formula assumes that:

Each payment is made at the end of the period
The interest rate remains constant
Payments are reinvested at the same rate

Formula

The future value of an ordinary annuity is calculated as:

FV = P × ((1 + r)^n – 1) / r

Where:

FV = future value of the annuity
P = payment per period
r = interest rate per period
n = total number of payments

Practical Example: Saving for a Business Equipment Upgrade

Step 1: Identify the inputs

P = $2,000
r = 6% annually ÷ 4 = 0.06 ÷ 4 = 0.015 per quarter
n = 5 years × 4 quarters = 20

Step 2: Apply the formula

FV = 2,000 × ((1 + 0.015)^20 – 1) / 0.015FV

= 2,000 × ((1.015^20 – 1) / 0.015)FV

≈ 2,000 × (1.346855 – 1) / 0.015FV

≈ 2,000 × 0.346855 / 0.015FV

≈ 2,000 × 23.1237FV

≈ $46,247.40

Interpretation

By consistently investing $2,000 each quarter for 5 years at a 6% annual interest rate (compounded quarterly), the company will have about $46,247 available for equipment purchases.

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The future value of an annuity helps quantify how much a series of regular payments will grow to over time, assuming reinvestment at a fixed interest rate. It’s particularly useful for budgeting long-term goals, from capital expenditure planning to personal savings strategies.

To apply it effectively:

Use consistent time periods (monthly, quarterly, etc.)
Ensure the interest rate matches the frequency
Use realistic assumptions on returns and duration