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The present value of an annuity can be calculated by:

                                               

Or to use the tables the change would be:

Present Value = Annuity * (Present Value Annuity Factor_n,i)

Let us see an example

Example

You have been promised an annual grant of Rs 7000 every year for the next 20 years if you can invest the amount at 5% per annum compounded annually what will be the amount you would require today to land up with the same position?

Solution

Here i = 0.05, A = 7000, and n = 20. Putting it in the formula we get:

                                               

Using the shortcut from the table we get:

                             PV = 7000 x 12.4622 = Rs 87,235.4

We looked at the present value of an annuity of Rs 1 for 20 years at 5% interest in the Present Value Annuity Factor Table given at the end of this book (i.e. find the value of Present Value Annuity Factor n,i)and found the figure to be 12.4622 (try finding the figure yourself) and then substituted the figure here to get the answer. Another way of doing it would be to use a scientific calculator and calculate the value that comes out to be the same.