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After compounding has been applied, the effective annual interest rates (EAR) are the annual interest rates received from any investment or savings that pays interest. If you don't know, compounding or interest, refers to the process where one's principal invests grows over time, as interest is added. If you invest RS. You'd get Rs. 1000 if you invest RS. 50 percent of the interest earned by the end the year. The interest would be added to the principal, thereby increasing it to Rs. The next year, the principal would be increased to Rs. 1050. The cycle continues. You can see that your accumulated interest for next years would be greater than previous years, because your principal has grown. This is a common phenomenon that causes exponential growth and snowballs over time.

When advertising their services, banks often advertise the nominal interest rate they offer for savings accounts. The effective interest rate is advertised alongside the nominal rate to better reflect real returns. Additional fees, etc. are also included in the effective annual rate. Required

This formula calculates the effective annual interest rates for savings and investment accounts.

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

- The nominal interest rate is represented by "i".
- "n" is the number of periods or time periods.

Let's look at an example.

Let's suppose that an individual deposits 10,000 Rupees into their savings account at an annual interest rate of 12.5%, compounded monthly.

You may think that you will have Rs. 1200 in Interest If you do the calculation with monthly compounding, you will see that you accumulate interest of Rs. This would give you an EAR of 12.7%.

The effective interest rate formula can confirm this:

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

This would be equivalent to 0.1268 or 12.7% interest, rounded off.

The nominal interest rate at first was 12%. However, we were able to calculate the effective annual rate formula which gives us the actual rate of return, which is 0.7 percent higher than the nominal rate.

This formula can be used in real-world situations, such as when choosing a bank to borrow from or a savings account. Banks tend to place a greater emphasis on the effective annual rate for savings accounts than the nominal rate. Customers feel that they are getting a higher rate of interest. Advertising loans may also advertise the nominal interest rate to give the impression that the borrower is receiving lower interest rates. Although the interest rate varied by less than 1 percent in the above example, any increase in the period of time would have a significant effect on the interest rates. Therefore, it is important to thoroughly review the clauses and details regarding interest rates before signing up for any service.

Let's look at another example: one could compare the savings accounts offered by two banks.

Two options are presented to a customer who wants to deposit 20,000 rupees in a savings account.

Bank A offers a 11% interest rate that is compounded semi-annually. Bank B offers a 11% interest rate that is compounded monthly.

Bank A's effective interest rate formula would therefore be (1 + 0.11/2), 2 – 1, or 11.30%.

The effective interest rate formula can also be converted to the annual effective rate formula by changing the variable "n" to the value of one or more time periods.

The effective annual interest rate formula of bank B would be therefore (1+ 0.11/12) + 12 -1, or 11.6%

Now the customer has a better understanding of what interest rates they might actually receive and can make an informed decision.

This principle can be used to the securities market, where investors want to invest in bonds. An investment of 10,000 in a bond that offers a semi-annual 6% interest rate would yield a return of 300 Rupees within the first six months. The investor would get 390 in the 6th month. The nominal interest rate is 6% but the effective rate formula shows that it is 6.9%.

The most important benefit of using an effective annual interest rate formula is that it provides a more accurate representation of the interest rate one would get from an investment, savings account, or other financial instrument. The effective interest rate is most commonly used in the bond market. It allows investors to calculate the real rate of interest for a given time period based on the actual asset.