# How Do You Calculate the Present Value of an Annuity Due?

## Two Approaches: Formula and Spreadsheet

An annuity due is a series of equal consecutive payments that you are either paying as a debtor or receiving as a lender. This differs from an annuity, as an annuity is a form of investment. Annuities are paid at the end of a period, while an annuity due payment is made at the beginning of a period. This payment covers the period to come.

Some examples of this could be a premium on insurance or rent due. If you were renting a house to someone, their monthly payments are an annuity due.

## Time Value of Money

Present value can be a difficult topic to digest. It refers to a concept called "the time value of money". Time value of money can be explained thusly—if you were given $1 today, it is worth more than the same $1 five years from now. This is due to the changing value of money and inflation, and the potential of money to earn interest.

The present value of an annuity due (PVAD) is calculating the value at the end of the number of periods given, using the current value of money. Another way to think of it is how much an annuity due would be worth when payments are complete in the future, brought to the present.

## Calculating the PVAD

For this formula, the following values are used:

P = periodic payment

r = rate per period

n = number of periods

The formula used is:

PVAD = P + P [ (1 - (1 + r)^{- (n - 1) }) ÷ r ]

For example, an annuity due's interest rate is 5%, you are promised the money at the end of 3 years and the payment is $100 per year.

Using the present value of an annuity due formula:

(100 + 100 [ (1 - (1 + .05)^{- (3 - 1) }) ÷ .05 ]

(100 + 100 [1 - (1.05)^{- 2}÷ .05 ] = $285.94

The value of $285.94 is the current value of three payments of $100 with 5% interest.

Using a spreadsheet application is more efficient when calculating present value if you are not familiar with the formula.

## Spreadsheet Calculation

Spreadsheets are designed to calculate present values and other financial calculations. The function used for the present value of an annuity due on a spreadsheet is:

=PV(rate,n,pmt, type)

The previous example would be entered as:

=PV(.05,3,-100,,1)

Microsoft Office, OpenOffice, and LibreOffice are examples of applications with spreadsheets. The formula is the same for all. It is listed as PV(i, n, pmt, FV, type). However, please note that the FV value is not used when calculating the present value of an annuity due. In this case, you would enter =PV(i,n,pmt,,type)

i = rate, or r

n= number of periods

pmt = amount of payment

For type, use 1. Type refers to when in the period the payment is made. 1 = the beginning, 0 = the end.

To enter the formula, open a worksheet, click on the cell you wish to enter it in. Press the equal sign, then enter PV. A hint will appear, informing you of function the formula performs.

Enter the example shown above, and press enter. The result should be the same as in the formula calculation.