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How do you Calculate the Present Value of an Ordinary Annuity?

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Question: How do you Calculate the Present Value of an Ordinary Annuity?

There are three approaches to solving the problem of calculating the present value of an single amount, one type of time value of money calculation. First, you can use the present value of an ordinary annuity formula. Second, you can use a financial calculator. Just about any financial calculator will do and will follow just about the same steps. Third, you can use a spreadsheet application, such as Excel. We will explore all three approaches.

Answer:

The Problem and The Formula

The first thing to remember is that present value of an is the exact opposite of future value of an annuity. Here is the formula:

PVAN = PMT [1/I) - 1/1/I(1+I)N

Consider this problem:

What is the present value of an ordinary annuity if the interest rate is 5 percent and you are promised the money at the end of 3 years if the payment is $100 per year?

Using the present value of an ordinary annuity formula:

PVA3 = 100 [1/0.05 - 1/0.05(1+0.053] = $272.32

Calculating present value is called discounting. Discounting cash flows, like our $100 yearly annuity, simply means that we take inflation and the fact that money has the ability to earn interest into account. Since you do not have the yearly $100 annuity in your hand today, you cannot earn interest on it so it is discounted today and is worth only $272.32.

Clearly, using the formula is the long way to do present value problems. Using a financial calculator or a spreadsheet application is a more efficient way to calculate present value.

Present Value of an Ordinary Annuity Using a Financial Calculator

You can find the present value of a ordinary annuity with any calculator with an exponential function, even non-financial calculators. It is best to use financial calculators because they have five keys that correspond to the five variables in time value of money equations. This present value of a single amount equation that we calculated above uses only four of those variables. Look at your financial calculator. Here are the key and inputs that you punch:

Punch N and 3 (for 3 years)

Punch I/YR and 5 (for the interest rate of 5%)

Punch PMT and -100 (be sure and make it a minus 100)

Punch PV and you will have your answer of $272.32

Present Value of a Ordinary Annuity Using a Spreadsheet

Spreadsheets, such as Microsoft Excel, are suited for calculating time value of money problems and other mathematical functions. The function that we use for present value of an ordinary annuity on an Excel spreadsheet is:

=PV(rate,N,pmt,fv) OR

=PV(0.05,3,-100,0)

Specifically, you go to an Excel worksheet and click on Financial function. You will pull down a menu and click on PV. That will open a box and you will fill out the information for the problem you are trying to solve. In the example we are using, you fill out the interest rate of 0.05, the time period of 3 (year), payments of -100, and a 0 for the last item which means that any payment would be at the end of the time period if we had payments. 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.

This online calculator will help you with practicing calculations for present value of a ordinary annuity.

These are the three ways to calculate present value of an ordinary annuity.

See these articles for more on time value of money:

  • Overview of Time Value of Money
  • Future Value of an Investment
  • Present Value of a Lump Sum
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