Limited Time Offer: Save 10% on all 2022 Premium Study Packages with promo code: BLOG10

Calculating Effective Annual Rate Given Stated Annual Interest Rate and Compounding Frequency

Calculating Effective Annual Rate Given Stated Annual Interest Rate and Compounding Frequency

The effective annual rate of interest (EAR) refers to the rate of return earned by an investor in a year, taking the effects of compounding into account. Remember, compounding is the process by which invested funds grow exponentially due to both the principal and the already accumulated interest, earning more interest. In other words, interest earned itself earns more interest. Mathematically, we may define EAR as follows:

$$ \text {EAR} = \left (1+ \text {Periodic rate} \right)^\text {m} – 1 $$

Where, $$\text {Periodic rate} = \frac {\text {Stated annual rate}} {m}$$

And \(m\) is the number of compounding periods per year.

Example: Semi-Annual Compounding

Imagine that you have been tasked to calculate the EAR, given a stated annual rate of 10% compounded semi-annually. You would be expected to directly apply the above formula.

$$ \text {EAR} = \left ( 1+ \text {periodic rate} \right)^\text{m} – 1 $$

Establishing the components already known,

Stated annual rate = 0.1

\(m\) = 2

Periodic rate = 0.1/2 = 0.05


$$ \begin{align*} \text {EAR} & = (1+ 0.05)^2 – 1 \\ & = 10.25\% \end {align*} $$

Example 2: A Range of Compounding Frequencies

Using a stated annual rate of 12%, compute the effective rates for daily, monthly, quarterly, and semi-annual compounding periods.

$$ \begin {align*} & \text {Semi-annual compounding} = (1+0.06)^2 -1= 0.1236 = 12.36\% \\ & \text {Quarterly compounding} = (1+0.03)^4 -1 = 0.12551 = 12.55\% \\ & \text {Monthly compounding} = (1+ 0.01)^{12} -1 = 0.12683 = 12.68\% \\ & \text {Daily compounding} = (1+0.00032877)^ {365} -1 = 12.75\% \\ \end {align*} $$

First, you should note that the compounding frequency and the EAR increase concurrently.

Furthermore, the stated rate is equal to the EAR only when the interest is compounded annually.

Why is the Effective Annual Rate of Interest Important?

The EAR is an important concept in financial management because it is used to compare two or more projects that calculate compound interest differently. For example, assume that you have two projects, X and Y. Project X pays 5% interest compounded monthly, while project Y pays 5% interest compounded quarterly. By calculating the EAR represented by each of these two rates, you would be able to pick the more profitable project of the two. Furthermore, the higher the EAR, the higher the return offered by an investment.


John Ross, a financial analyst, would like to have $20, 000 saved in his bank account at the end of 5 years. The bank offers a return of 10% per annum compounded semi-annually. The annual effective rate of return applicable to Ross’ investment is closest to:

  1. 5.00%.
  2. 5.13%.
  3. 10.25%.


The correct answer is C.

The question asks us to find the effective rate of return. We, therefore, have to determine the value of \(r\), which will be the EAR:

$$ \begin{align} EAR & = { 1+ (\frac {0.1}{2} ) }^2 – 1 \\ & = (1+0.05)^2 -1 = 10.25\% \end{align} $$

A is incorrect. It assumes the following calculation:


B is incorrect. It assumes monthly compounding and not semi-annual compounding in determining the EAR as follows:



Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop GMAT® Exam Prep

    Sergio Torrico
    Sergio Torrico
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.