Future Value of Ordinary Annuity

\[FV=PMT\frac{(1+i)^n-1}{i}\]

Variables

FVfuture value of annuity (currency)

PMTperiodic payment (currency)

iinterest rate per period (decimal)

nnumber of periods

Description

What is this formula?

The Future Value of an Ordinary Annuity calculates the accumulated value of a series of equal payments made at the end of each period, assuming compound interest.

Each payment earns interest for a different amount of time depending on when it is deposited.

When to use it

Use this formula when regular deposits or payments are made at the end of each period and you want to determine the accumulated future value.

Example

Suppose:

PMT = $1,000

i = 0.01 per month

n = 12 months

Formula:

FV=PMT((1+i)^n−1)/i

Substitution:

FV=1000((1.01)^12−1)/0.01

FV=12,682.50

Result:

Future Value = $12,682.50

Applications

Retirement planning

Savings plans

Investment analysis

Pension calculations

Education funds

Financial planning

Note

This formula assumes equal payments and a constant interest rate throughout the entire investment period. Real-world investments may experience changing interest rates, taxes, fees, or irregular contributions that affect the actual accumulated value.