Introduction

The interest rate has many types in finance: real, nominal, effective, annual and so on. The difference between Nominal and Effective Rates (Two of the most used types of rates) is based on various economy factors and can generate a serious dollar value difference, and therefore, it is extremely important to understand the difference and be able to calculate it quickly and easily.

The Nominal interest rate, the simplest type of rate, is referred to as the coupon rate for fixed income interest and represents the actual amount of money to pay. For example, if the loan is $100 and the nominal rate is 5%, the borrower will expect to pay $5.

The Effective interest rate is a bit more complex as it takes the power of compounding into account. For example, if an investment pays 2.5%  as a nominal Interest rate and compounds semi-annually, the investor who placed $1000 will receive $25 after the first 6 months (1000 x 0.025) and $25.625 after a year (1025 x 0.025), and this means the investor received an effective interest rate of 2.5625%. So, you can see that the Effective Interest rate will yield more interest than the nominal interest rate as it takes the power of compounding for the loan/investment into account.

Now that we have established what an Effective rate and a Nominal rate was, we can see how easily we can convert them using the NOMINAL() or the EFFECT() function.

 

Syntax and Arguments

The nominal() function

Syntax: NOMINAL(effect_rate, npery)

  • effect_rate: Refers to the effective interest rate
  • Npery: The number of periods per year

The effect() function

Syntax: EFFECT(nominal_rate, npery)

  • nominal_rate: Refers to the Nominal interest rate
  • Npery: The number of compounding periods per year

As we can see above, the only variable that affects the difference between Nominal and Effective rate is the number of compounding periods (as it increases, the difference between the rates widens).

 

NOMINAL function (To convert from Effective to Nominal interest rate)

Let’s assume we want to know the nominal interest rate of a loan, in which its effective interest rate is 6% and the payments are required monthly. The information we have is as below:

.

In order to calculate the nominal function, we will need to input the following formula: NOMINAL(C5,C6), where C5 is the effective interest rate and C6 is the compound period.

We will obtain 5.84%, which is less than the Effective annual rate as it does not take the compounding into account.

 

EFFECT function (To Convert from Nominal to Effective tinterest rate)

In this example, we have the nominal rate of a loan, 7% and the payment is required bi-monthly (6 times a year). The information we have is as below:

The formula we use is EFFECT(H5,H6), where H5 is our Nominal interest rate and H6 is our compounding periods

Our result is 7.21%, and we can notice that as expected, it is higher than the nominal interest rate.

 

Understanding the correlation

As we have mentioned earlier, the Effective interest rate takes the power of compounding into account, meaning the more payments are made over a year, the higher the Effective rate will be for the same Nominal rate. As an example, we have taken a fixed Nominal interest rate of 7% and analyzed the evolution of the Effective rate depending on the compound periods: Annual, quarterly, monthly or Weekly. We can see that the more frequent are the payments, the higher is the Effective rate.

As an example, we have taken a fixed Nominal interest rate of 7% and analyzed the evolution of the Effective rate depending on the compound periods: Annual, quarterly, monthly or Weekly. We can see that the more frequent are the payments, the higher is the Effective rate.

 

Conclusion

Knowing the difference between Nominal and Effective rate is crucial in the world of finance, whether you are investing or borrowing. For example, as we have proven earlier, a loan with frequent compounding periods will end up more expensive than one that compounds annually. On the other hand, an investment that promises a certain Nominal rate with only an annual compounding will not be as interesting as the same rate with a weekly return.

Even though the difference can seem very small (and it will often be the case for small amounts and small time periods), the rate difference will have more impact on larger amounts, and just a change between quarterly and monthly payment can have a massive impact on the total interest value.


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Abdelrahman Abdou
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