### An Annuity Due

An annuity due is a series of equal consecutive payments just like an ordinary annuity. The difference between an annuity due and an ordinary annuity is that an annuity due is paid at the beginning of a time period. An example is a lease payment. An ordinary annuity is paid at the end of a time period. Since the annuity due is discounted for one less time period than the ordinary annuity, the present value of an annuity due is less than that of a comparable ordinary annuity.

### How to Calculate the Present Value of an Annuity Due

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.

### The Formula for Calculating the Present Value of An Annuity Due

Here is the formula:

**PVA _{DUE} = PMT [1/I) - 1/1/I(1+I)^{DUE (1 + I)}**

The difference in this formula and the formula for present value of an annuity due is the (1 + I) term at the end of the equation. This adjusts for the fact the annuity due is paid at the beginning of the time period.

Consider this problem:

What is the present value of an annuity due 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 annuity due formula**:

**PVA _{DUE} = 100 [1/0.05 - 1/0.05(1+0.05^{3}] (1 + 0.05) = $285.94**

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 $285.94, a little more than you earn on the ordinary annuity.

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.

### Calculating Present Value of an Annuity Due 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. You use the same variables as for the ordinary annuity except you set your calculator to **BEGIN MODE**. 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 $285.94**

### Present Value of an Annuity Due 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 annuity due on an Excel spreadsheet is:

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

**=PV(0.05,3,-100,1)**

Type 0 is for an ordinary annuity while Type 1 is for an annuity due.

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 1 for the last item which means that any payment would be at the beginning 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 $285.94.

### **More to Learn About Time Value of Mone****y**

How to Calculate Present Value of an Ordinary Annuity How to Calculate the Present Value of a Single Amount Time Value of Money: Overview of Discounted Cash Flow Analysis