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(^36) Financial Management
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:
Future Value = 




 + -
i
A [(^1 i)n^1 ]
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 text book
to calculate the compound values of the cash flows and the formula would change to:
Future Value = Annuity * (Future Value Annuity Factorn,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:
Fugure Value = 




 + -
0. 05
7000 [(^10.^005 )^201 ]
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.
Let us see how we use Microsoft Excel to do the same. Insert the values as given in
the example. Here r = I = 0.05, Nper is the number of periods = 20, Pmt is the periodic
annuity = 7000. Pv is the present value = 0 in this case as it an annuity and Type is a
value representing the timing of the payment = 0 in this case as the first investment is