### What is Annuity ? - Meaning and Concept

An annuity, just like a perpetuity, is a shortcut used while making present value calculations. Unlike the perpetuity, which is very difficult to find in real life, we find examples of annuity all around us. The monthly mortgage payments we make, the car loan or student loan that we pay off are all annuities. Annuities play a very important role in corporate finance. They form the basis for valuation of bonds and other financial instruments. This article provides more information about the concept of an annuity:

Finite Stream: The first and foremost difference between an annuity and a perpetuity is the fact that an annuity has a finite life. Unlike perpetuities, annuities do not go on forever. It is for this reason that we they are conceptually more intuitive and easy to understand.

Equal Amounts: A stream of payments can be called an annuity, if and only if, all the payments in that stream of future cash flows is of equal amounts. For instance, if the future cash flows for 4 consecutive years from now are \$100 in each year, then this stream is called an annuity. On the other hand, if the future cash flows for the next 3 years are \$100 and the 4th year is \$110, then this stream of cash flows cannot be called an annuity. (It is an annuity if you consider years 1 to 3)

Equal Time Lag: Every payment in the stream of cash flows should be equally spaced. This means that if payments are being made on a monthly basis, all payments should be made on a monthly basis. If the time lag when payments are made is changing, then the cash flow schedule cannot be classified as an annuity. This is because the annuity formula assumes that the cash flows are evenly spaced out.

Same Interest Rate: A stream of cash flows can be called an annuity, if the interest rate being charged throughout the period is same. For instance, if the rate of interest across the entire duration of a 10 year loan is 10%, then the stream of payments can be classified as an annuity. On the other hand, if the rate of interest keeps varying from year to year, then it cannot be valued as an annuity because the annuity calculation formula assumes the same interest rate.

Amortization Concept: The payments in an annuity represent amortization of a lump sum amount. This means that although the amount paid in installments is constant, its internal components are changing.

Let’s understand this, with the help of an example. Let’s say that there is a \$100 payment per month for the next 5 years. Now, the \$100 amount will remain constant for the next 5 years, however the internal components will change. The first payment may represent an \$80 interest charge and \$20 repayment of principal while the last payment may only represent \$10 interest and \$90 repayment of principal. This is called amortization.

The first few payments in an annuity have very high interest components. With the passage of time, the interest component becomes smaller and smaller and repayment of principal amounts becomes larger and larger.