FREE online courses on Investment Appraisal - Basic Concepts of Investment Appraisal - Future Value of an Annuity

 

Annuity is defined as periodic payment every period for a number of periods. This periodic payment is the same every year only then it could be called an annuity. The compound value (future value) of this annuity can be calculated using a different formula:

                                               

Here A is the constant periodic cash flow (annuity), i is the rate of return for one period and n is the number of time periods. The term within the brackets is the compound value factor of an annuity. We can also use the tables given at the end of the textbook to calculate the compound values of the cash flows and the formula would change to:

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

Extending the same example we used above, if we were going to pay Rs 7000 every year for the next 20 years what is the value at the end of 20 years if the interest rate was 5 % compounded annually.

Example

 

An annual payment of Rs 7000 is invested at 5% per annum compounded annually. What will be the amount after 20 years?

Solution

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

                                     

                             FV = 7000 x 33.066 = Rs 2,31,462

 

We have taken a shortcut here. We looked at the future value of Rs 1 at the end of 20 years at 5% interest in the Future Value Annuity Factor Table given at the end of this book (i.e. find the value of Future Value Annuity Factor n,i)and found the figure to be 33.066 (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.