Present Value of Annuity Calculator

How to Calculate Present Value of Annuity

The present value of an annuity is a fundamental concept in finance that helps individuals and businesses determine the current worth of a series of equal payments to be received in the future. This guide will walk you through the process of calculating the present value of an annuity.

Present Value of Annuity Formula

There are two main types of annuities: ordinary annuities and annuities due. The formulas for each are slightly different:

Ordinary Annuity (Payments at the end of each period):

$$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$$

Annuity Due (Payments at the beginning of each period):

$$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \times (1 + r)$$

Where:

• PV = Present Value of the Annuity
• PMT = Regular Payment Amount
• r = Interest Rate per Period
• n = Total Number of Periods

Calculation Steps

1. Determine the type of annuity (ordinary or due).
2. Identify the regular payment amount (PMT).
3. Calculate the interest rate per period (r) by dividing the annual interest rate by the number of compounding periods per year.
4. Calculate the total number of periods (n) by multiplying the number of years by the number of payments per year.
5. Apply the appropriate formula based on the annuity type.
6. Calculate the result to find the present value of the annuity.

Example Calculation

Let's calculate the present value of an ordinary annuity with the following characteristics:

• Regular Payment (PMT): $1,000
• Annual Interest Rate: 5%
• Number of Years: 5
• Payments Made: Annually (at the end of each year)

Step 1: Identify the variables

• PMT = $1,000
• r = 5% = 0.05 (annual rate, compounded annually)
• n = 5 years

Step 2: Apply the ordinary annuity formula

$$PV = 1000 \times \frac{1 - (1 + 0.05)^{-5}}{0.05}$$

Step 3: Calculate the result

$$PV = 1000 \times \frac{1 - 0.7835}{0.05} = 1000 \times 4.3295 = $4,329.50$$

Therefore, the present value of this annuity is $4,329.50.

Visual Representation

This line chart illustrates how the present value of the annuity changes over the 5-year period. The value increases as we move closer to the present, reflecting the time value of money.