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What is Ordinary Annuity?

Arjun Kulkarni Jun 18, 2019
Ordinary annuity being a fixed payment, is subject to a few rules. You need to follow them while paying the annuity for something. Here's what you have to do.
An ordinary annuity is a fixed payment at the end of a period towards an expense. The best example is a mortgage loan. Once you take a mortgage loan, at the end of every month, you're supposed to pay a certain pre-decided amount towards mortgage payments. Ordinary annuity is thus a series of payments paid to cover some sort of expense.

Present Value of an Annuity

But of course, there's more to an annuity than simply the part mentioned here. Ordinary annuities can be subdivided into two main types: present value of an annuity and future value of an annuity. Present value of an annuity is the present value (today's value) of future annuity cash flows. Why would you calculate present value of an annuity?
Let us try and understand this concept with the help of a typical textbook financial management example which uses the concept of time value of money. Now suppose you want to invest in some fund which asks for a certain amount up front, and promises you a return of some interest each year for the next 5 years.
Now how would you evaluate this investment proposition? You will need the two amounts: fixed amount to be paid and the regular yearly interest payments. You will also need to decide your rate of return, the percentage of return which you expect your investment to earn.
Now if the investment decision is a good one, then the present value of the interest stream should be MORE than the money you're investing today. Why? Because since the value of money today is more than the value of money after five years, you obviously want a return which is higher in the future than the amount of money you have today.
So in present value of annuity, you calculate the present value of future inflows, discounted at the rate of return expected and hope that the amount is more than the money you're putting in today.
Confused? Well, this formula for present value of an ordinary annuity ought to put things in order!

Present Value of Annuity = Amount received each year (1 - (1 + i)-n)

where i= rate of return/100 and n= number of years.

Future Value of an Annuity

Future value is quite simply, the opposite of the case mentioned here. In the future value of an annuity calculation, you have to flip the example given here. The calculation for the future value of an annuity gives you the final value of the annuities paid hence for a few years, at the end of the payment period.
Let us take the example of an investment where you are supposed to pay certain amount of money each year to the company and at the end of the period, they offer you a larger amount. How would you know if the amount they offer at the end of the period is good enough?
The future value formula takes into consideration the fact that an amount of money in the future has lesser value than the same amount of money today. So the amount to be received at the end of the payment period ought to be more than the summation of the amounts paid. How much more? That depends on the interest rate you think is reasonable.
With the help of the formula given further, you will be able to find out the future value of the amounts paid hence. If the final amount on the left hand side in this formula is less than what you're being offered, then the amount offered is more than what you expect and hence, you ought to take it!

Future Value = Periodic Interest Payments [(1 + i)n - 1]
At last, it is nothing but annuity paid/received at the end of the period. Then what about ordinary annuity vs annuity due? Annuity due is simply the annuity paid at the start of the period.