Calculate the Present Value of an Ordinary Annuity

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Three approaches exist to calculate the present value of a single amount, known as a time value of money calculation. You can use a formula and regular calculator to figure out the present value of an ordinary annuity. You can also use a financial calculator, and you'll follow basically the same steps. Additionally, you can use a spreadsheet application, such as Excel and one of its built-in financial formulas.

The Formula

Use the following formula to calculate an annuity's present value:

Present value of annuity = P [1 - (1 + r) ^(-n) / r]

Where:

P = periodic payment

r = periodic interest rate

n = number of periods

It's important to note that this equation assumes the payment and interest rate do not change for the duration of the annuity payments.

Example

Say you want to calculate the present value of an ordinary annuity with an annual payment of $100, an interest rate of 5 percent and you are promised the money at the end of 3 years. 

Using the present value of annuity formula, you would calculate the amount as follows:

Present value of annuity = $100 [1 - (1 + .05) ^(-3) / .05] = $272.32

When calculating the present value of an annuity, you are discounting the annuity's value. Discounting cash flows, such as the $100-per-year annuity, means the calculation considers inflation, risk over time and the inability to earn interest on money that you don't yet have as factors that reduce the value of future dollars in relation to money in your pocket today. Simply put, since you do not have the yearly $100 annuity in your hand today, you can't earn interest on it so it's discounted today to a value of only $272.32.

Using the above formula to work present value problems takes a little time. You can use a financial calculator or a spreadsheet application to more efficiently calculate present values.

Present Value of an Ordinary Annuity Using a Financial Calculator

You can find the present value of an ordinary annuity with any calculator that has an exponential function, even non-financial calculators.

Financial calculators make things easier because they have individual keys that correspond to the five variables in time-value-of-money equations. This present value equation that we calculated above uses only four of those variables. On a financial calculator, you would use the following keys and inputs:

  • Press N and 3 (for 3 years)
  • Press i or I/YR and 5 (for the interest rate of 5 percent)
  • Press PMT and -100 (be sure and make it a minus 100)
  • Press  PV and you will arrive at your answer of $272.32

Present Value of an Ordinary Annuity Using a Spreadsheet

Spreadsheets, such as Microsoft Excel, work well for calculating time-value-of-money problems and other mathematical equations. You can type the equation yourself, or use a built-in financial function that walks you through the formula inputs.

Using the same inputs as above, you would use the following formula for present value of an ordinary annuity in your Excel spreadsheet, remembering to enter your $100 payment as a negative number:

=PV(rate,nper,pmt) 

=PV(.05,3,-100)

To locate the formula instead of typing it in, go to an Excel worksheet and click on Financial function on the Formulas menu.

View the drop-down menu and click on PV. You'll see a dialogue box open with spaces for each input, for you to fill out the information for your PV calculation.

Using the previous inputs, fill out the interest rate of 0.05, the time period of 3 (year), and payments of -100, 

You end up with the function above. Then, you go to the right-hand side of the worksheet at the top and click on Calculate. You will get the answer of $272.32.

You can use this ​online calculator ​to help you double-check your calculations for the present value of an ordinary annuity.