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EAR vs. APR

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Written By
Dan Buckley
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Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
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Updated
May 2, 2023

Understanding the difference between the Effective Annual Rate (EAR) and the Annual Percentage Rate (APR) is important when navigating the world of loans and credit.

Both rates are used to determine the cost of borrowing, but they are calculated differently and serve distinct purposes.

This article will provide an understanding of EAR and APR, their differences, and how they impact your financial decision-making.

 

Key Takeaways – EAR vs. APR

  • Effective Annual Rate (EAR) and Annual Percentage Rate (APR) are both used to determine the cost of borrowing, but they are calculated differently and serve distinct purposes.
  • EAR accounts for the effect of compounding interest, whereas APR does not. As a result, EAR tends to be higher than APR when compounding occurs more frequently than annually.
  • APR is primarily used for comparing the cost of different loans and credit cards, while EAR is used to determine the actual return on an investment or the real cost of borrowing when interest is compounded more frequently than annually.

 

EAR: Effective Annual Rate

The Effective Annual Rate (EAR) – also known as the annual equivalent rate (AER) or effective interest rate – represents the actual annual cost of borrowing or return on investment, taking into account the effect of compounding interest.

Compounding is the process of adding interest earned on an investment to the principal amount, resulting in interest earned on both the initial amount and the accumulated interest.

When compounding occurs more frequently than once per year, such as daily, monthly, or quarterly, the EAR will differ from the nominal interest rate.

EAR Formula

The formula for calculating EAR is as follows:

 

EAR = (1 + i/n)^(n) – 1

 

Where:

  • EAR = Effective Annual Rate
  • i = Nominal annual interest rate
  • n = Number of compounding periods per year

 

APR: Annual Percentage Rate

The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing, as it includes not only the interest rate but also additional fees and charges associated with a loan.

APR is designed to give borrowers a more accurate picture of the total cost of a loan over its entire term, expressed as an annualized percentage.

APR is commonly used to compare various loan offers and credit card rates.

It is regulated by the Truth in Lending Act, which requires lenders to disclose the APR to borrowers.

APR Formula

The formula for calculating APR is as follows:

 

APR = (Total Finance Charges / Loan Amount) / Loan Term * 365 * 100

 

Differences between EAR and APR

Interest compounding

EAR accounts for the effect of compounding interest, whereas APR does not.

As a result, EAR tends to be higher than APR when compounding occurs more frequently than on an annual basis.

Additional costs

APR incorporates fees and other charges associated with a loan, giving borrowers a more accurate representation of what the total cost of borrowing is.

EAR only considers the interest rate and compounding effect.

Purpose and usage

APR is primarily used for comparing the cost of different loans and credit cards.

On the other hand, EAR is used to determine the actual return on an investment or the real cost of borrowing when interest is compounded more frequently than annually (e.g., continuously, daily, monthly, quarterly).

 

Time Value of Money (APR vs. EAR)

 

Conclusion – EAR vs. APR

Understanding the difference between EAR and APR is essential when making informed financial decisions, especially when it comes to loans and credit.

While EAR reflects the true annual cost of borrowing or return on investment by considering the effect of compounding interest, APR provides a more comprehensive view of the cost of a loan by including fees and other charges.

By distinguishing between these two rates, borrowers and investors can better evaluate loan offers, credit card rates, and investment opportunities, ultimately making smarter financial choices.