# Effective Annual Interest Rate

The effective annual interest rate (EAR) is the annual interest rate received from any investment/saving that pays out interest, once it has been adjusted for the appropriate compounding.  If you aren’t aware, Compounding, or compounding interest, is the process by which one’s principal invested grows larger over time as accumulated interest is added to it. For example, if you invest RS. 1000 rupees today, which compounded annually, you’d have Rs. 50 of interest by the end of the year. This would then be added to your principal increasing it to Rs. 1050 for the next year. The cycle then repeats. As you can see, your accumulated interest for next year would be higher than the previous years because your principal has also grown. This tends to snowball over time and results in exponential growth.

Banks, when advertising their services, often advertise their nominal interest rate for a savings account for instance. However, it is the effective interest rate advertised alongside the nominal interest rate that is a more accurate representation of real returns. Additionally, the effective annual interest rate also reflects any additional fees etc. required.

Calculating Effective Annual Interest Rate

The effective annual interest rate for any investment or savings account can be used by employing the following effective annual interest rate formula:

Effective annual interest rate = (1 + i / n) ^ n -1.

• “i” represents the nominal interest rate
• “n” reflects the time period, or number of periods.

Let’s take an example.

Let’s say an individual deposits 10,000 rupees in their savings account, at an Annual interest rate of 12%, which is compounded monthly.

It may seem that, by the end of the year, you would have Rs. 1200 in Interest. However, if one does the calculation with monthly compounding you see that you get accumulated interest of Rs. 1268.25 implying an EAR of about 12.7%.

This can be confirmed by the effective interest rate formula:

Effective Interest Rate = (1 + 0.12/12) ^ 12 -1

This would equal to 0.1268, or 12.7% interest when rounded off.

Therefore, while the nominal interest rate was initially 12%, applying the effective annual interest rate formula helped us arrive at the effective interest rate, or your actual rate of return which is 0.7 % higher than the nominal rate.

This formula can be employed in a real-world scenario while choosing a savings account or bank to take a loan from for example. Traditionally, banks tend to, for their savings account, lay a larger emphasis on the effective annual interest rate, and less on the nominal rate, as customers feel like they are receiving a higher interest. Alternatively, when advertising loans, the nominal interest rate is advertised, as it gives the impression of lower interest rate payments for the borrower. While the example above saw the interest rate vary by less than 1%, an increase in the time period would have a significant impact on the interest rate and thus one should always make sure they check the interest rate details and clauses thoroughly before opting for any given service.

Let’s take another example wherein one might compare the offerings from two banks for a savings account.

A customer wishes to deposit 20,000 rupees into a savings account, and is presented with two options.

Bank A offers a 11 % interest rate which is compounded semiannually, whereas bank B offers an 11% interest rate, compounded monthly.

The effective interest rate formula for Bank A therefore would be: (1 + 0.11/2) ^ 2 – 1 ,  or 11.30%.

This effective interest rate formula can be turned into the effective annual interest rate formula, by fixing the variable “n”, to the value of one year, or one time period.

Therefore, the effective annual interest rate formula for bank B would therefore be (1+ 0.11/12) ^ 12 -1, or 11.6%

The customer now has a better idea of the interest rates they would realistically receive and can make a more informed decision.

This can also be applied to the securities market where investors are looking to invest in bonds for instance. If a certain bond offers a 6% interest rate semi – annually, an investment of 10,000 would give the investor a return of 300 rupees in the first 6 months. In the second 6, the investor would receive 390.  Therefore, while the nominal interest is 6%, the application of the effective interest rate formula shows us that the effective interest rate is in fact 6.9%.

Conclusion

The effective interest rate formula can be used to achieve the prime benefit of employing an effective annual rate; the fact that it offers a more real representation and accurate figure of the interest rate one would receive from an investment, savings account or any financial instrument. Most employed in the market of bonds, the effective interest rate allows investors to calculate the real interest rate for a certain time period, based on the actual value of that given instrument.