Present Value of Annuity Calculator

What is the Present Value of an Annuity?

The present value of an annuity is the current value of a series of future cash flows, given a specified rate of return or discount rate. It's a fundamental concept in finance that helps determine how much a series of future payments is worth in today's dollars.

The Present Value of Annuity Formula

The formula for calculating the present value of an annuity is:

\[PV = A \times \frac{1 - (1 + r)^{-n}}{r}\]

Where:

• \(PV\) = Present Value
• \(A\) = Annuity payment (the payment received each period)
• \(r\) = Interest rate per period (in decimal form)
• \(n\) = Number of periods

Step-by-Step Present Value of Annuity Calculation

1. Identify the annuity payment (A), interest rate (r), and number of periods (n).
2. Convert the interest rate to decimal form (divide by 100).
3. Plug these values into the present value of annuity formula.
4. Calculate the result to get the present value.

Example Calculation

Let's calculate the present value of an annuity with payments of $1,000 per year for 5 years, with an interest rate of 5% per year:

1. \(A = \$1,000\), \(r = 5\% = 0.05\), \(n = 5\) years
2. \[PV = 1000 \times \frac{1 - (1 + 0.05)^{-5}}{0.05} = \$4,329.48\]

Visual Representation

The green portion represents the present value ($4,329.48), and the blue portion represents the difference between the sum of all future payments ($5,000) and the present value ($670.52).