# Compounding vs annualised yield

India Infoline News Service / 12:02 , Oct 17, 2012

## Financial terms are usually difficult for lay investors to understand. It is important for investors to understand these some of these basic terms before investing, Sanjay Matai elaborates..

Open any newspaper today and you are likely to be bombarded with bank advertisements encouraging you to invest in their fixed deposits (FDs). Each bank is trying to out-do the other by offering very lucrative interest rates.

This competition is definitely beneficial for investors. However, in their anxiety to appear superior, some banks are resorting to ads that border on being unethical. The level of financial literacy in India is still low. And these ads are trying to exploit this weakness of an average investor. The unfortunate part of this whole story is that these are not some unknown banks. Rather, they are amongst the major ones.

Let us look at one such example. The below table provides information on the interest rates provided by some banks on their FDs—as mentioned in their ads in newspaper.

FD rates & how annualised yield is calculated

 Duration Interest rate APY* Maturity value Returns APY 1-2 years 9.25% 10.03% Rs. 12,007 Rs. 2,007 0.2007÷2 yrs = 10.03% 2-3 years 9.25% 10.52% Rs. 13,157 Rs. 3,157 0.3157÷3 yrs = 10.52% 3-5 years 9.25% 11.59% Rs. 15,798 Rs. 5,798 0.5798÷5 yrs = 11.59% 5-8 years 9.25% 13.48% Rs. 20,783 Rs. 10,783 1.0789÷8 yrs = 13.48% 8-10 years 9.25% 14.95% Rs. 24,954 Rs. 14,954 1.4954÷10 yrs = 14.95%
*Annualised percentage yield

Usually banks give you two options:
Simple interest rate
Compounding interest rate
The simple interest rate is usually easy to understand, as they advertise the rate of interest you will get for your deposit. However, the cumulative or compounding plan becomes confusing because they advertise an interest rate and an annual effective yield.

What is confusing?
The confusing part in the table is 14.95% for 10 years maturity. Our eyes naturally get attracted towards the highest number in the table i.e. 14.95% yield per annum for a 10-year FD. It appears as if the ‘annual return’ is quite high—14.95% for a 10-year deposit. In reality this is not so.

You are getting interest @ 9.25% per annum (payable every quarter). And because of this quarterly compounding, the effective return is 9.58% whatever may be the period of FD. This number (14.95%) is high only because Rs. 10,000 is compounded @ 9.25% for 10 years—which gives interest of Rs. 14,954. The interest amount (Rs. 14,954) is divided by Rs. 10,000—the original invested amount. The value 1.4954 is further divided by 10 years period that gives 14.95% simple interest rate or annual yield.

Thus, if you invest Rs. 10,000 in an FD at 14.95% for a year, you will get Rs. 1,1495. Now if you invest Rs. 10,000 (your principal again for nine years) @ 14.95%, you get Rs. 23,455. Add Rs. 23,455 + Rs. 1,495, the amount is Rs. 24,950.

Actually, the bank is calculating simple interest assuming as if your principal amount (Rs. 10,000) is constant throughout the 10-year period. However, this is not the case. Every year you are earning interest. This interest gets added to your principal. So every year your principal is increasing. Hence, applying the simple interest formula to a compounding investment is not correct.

If you keep your money for a long period, obviously your total amount on maturity will be high. If your maturity amount is more, naturally it will appear as if you have earned ‘more’ money. The higher maturity amount indicates that the interest rate offered on an FD was higher—if you apply simple interest rate or annualized percentage yield formula.

In short, we get an impression that we are getting a higher interest rate on our FD (14.95%). But actually, you are getting 9.25% per annum on your FD. Moreover, the interest rate is same for different periods. So logically how can the annualised yield be different? You can’t compare 14.95% with the interest rate (9.25%) that banks normally show since that’s like comparing apples and oranges. Therefore, it is important to understand the difference between compounding interest rate and annual yield while depositing your money.

The writer is the promoter of The Wealth Architects.