Present Value of Ordinary Annuity

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

Variables

PVpresent value of annuity (currency)

PMTperiodic payment (currency)

iinterest rate per period (decimal)

nnumber of periods

Description

What is this formula?

The Present Value of an Ordinary Annuity calculates the current value of a series of equal future payments made at the end of each period.

It represents the amount of money that would be equivalent today to receiving those future payments, considering the time value of money.

When to use it

Use this formula when evaluating loans, leases, pensions, bonds, retirement plans, or any financial arrangement involving equal periodic payments.

Example

Suppose:

PMT = $1,000

i = 0.01 per month

n = 12 months

Formula:

PV=PMT(1-(1+i)^(-n))/i

Substitution:

PV=1000(1-(1.01)^(-12))/0.01

PV=11,255.08

Result:

Present Value = $11,255.08

Applications

Loan valuation

Lease analysis

Bond valuation

Retirement planning

Pension calculations

Financial decision making

Note

This formula assumes equal payments and a constant interest rate throughout the annuity period. Real financial contracts may include variable rates, fees, inflation effects, or irregular payment schedules that alter the actual present value.