*The Business Professor*, updated November 30, 2018, last accessed June 2, 2020, https://thebusinessprofessor.com/lesson/effective-annual-interest-rate/.

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### Effective Annual Interest Rates Definition

An effective annual interest rate, also known as annual equivalent rate, effective rate, and effective interest rate, is a return that is earned on investments, loans, or other financial assets during a stipulated period of time. The rate differs from the stated annual percentage rate because of compounding of interest.

### A Little More on What is Effective Annual Interest Rate

The effective rate of return often differs from the nominal return. This is because interest earned is calculated (compounded) on a monthly, bi-monthly, semi-annual, or annual basis.

Suppose investment A has 10% return compounded monthly, and investment B has 10.1% compounded semi-annually. To determine which investment is more attractive and pays more return over the given time period, the effective interest rate can be used to assess which investment is more profitable.

The effective interest can be calculated by using the following formula;

= (1+i/n) ^n-1

i = annual interest fee

n = number of compounding years

The nominal interest rate in an interest rate stated on the face value of financial instruments. The nominal interest rate in the above example is 10% for investment A and 10.1% for investment B. An effective interest rate can be calculated by applying the above formula.

EAR for investment A would be: 10.47% = (1 + (10% / 12)) ^ 12 – 1

And EAR for investment B would be: 10.36% = (1 + (10.1% / 2)) ^ 2 – 1

From the above example, it can be seen that the investment has a higher nominal interest rate but it has a lower effective rate of investment due to fewer compounding period.

### References for Estimate Tax Combined

- https://www.investopedia.com/terms/e/effectiveinterest.asp
- https://en.wikipedia.org/wiki/Effective_interest_rate
- https://www.accountingcoach.com/blog/effective-interest-rate

### Academic Research on Effective Annual Interest Rate

● __The market model of ____interest rate ____dynamics__, Brace, A., G¸ atarek, D., & Musiela, M. (1997). *Mathematical finance*, *7*(2), 127-155. In this paper, a class of term structure models with volatility of lognormal type is analyzed in the general HJM framework.

● __Financial ____structure and the ____interest rate ____channel of ECB monetary policy__, Mojon, B. (2000). This paper analyses persistence differences in financial structure across countries of the euro area and whether they can lead to asymmetries in the transmission of the ECB policy.

● __The profit orientation of microfinance institutions and ____effective interest ____rates__, Roberts, P. W. (2013). *World Development*, *41*, 120-131. This study addresses the question of whether the sector benefits from microfinance institutions (MFIs) having stronger profit orientations by analyzing the relationship between interest rates and adopting the for-profit legal form, appointing private sector representation and traditional banking experience to advisory boards, and participating in more extensive for-profit networks.

● __On the predictive power of ____interest ____rates and ____interest rate ____spreads__, Bernanke, B. (1990). (No. w3486). National Bureau of Economic Research. In this paper, the authors examine a number of interest rates and interest rate spreads which have been found to be useful in prediction the course of the economy. The main aim of this paper is to show that the spread between the commercial paper rate and the Treasury bill rate has been a particularly good predictor. It also also shows that, possibly because of charges in monetary policy operating procedures aid in financial markets, this spread appears r to be a less reliable predictor than it used to be.

● __Corporate yield spreads and ____bond ____liquidity__, Chen, L., Lesmond, D. A., & Wei, J. (2007). *The Journal of Finance*, *62*(1), 119-149. This study shows that liquidity is priced in corporate yield spreads. Using a battery of liquidity measures covering over 4,000 corporate bonds and spanning both investment grade and speculative categories, it shows that more illiquid bonds earn higher yield spreads, and an improvement in liquidity causes a significant reduction in yield spreads. These findings justify the concern in the default risk literature that neither the level nor the dynamic of yield spreads can be fully explained by default risk determinants.

● __Government ____bond ____returns, measurement of ____interest rate ____risk, and the arbitrage pricing theory__, Gultekin, N. B., & Rogalski, R. J. (1985). *The Journal of Finance*, *40*(1), 43-61. Empirical tests are reported for Ross’ arbitrage pricing theory using monthly data for U.S. Treasury securities during the 1960–1979 period. We find that mean returns on bond portfolios are linearly related to at least two factor loadings. Multivariate test results, however, are not consistent with the APT.

● __Interest rate ____convergence in euro-candidate countries: Volatility dynamics of sovereign ____bond ____yields__, Gabrisch, H., & Orlowski, L. T. (2010). *Emerging Markets Finance and Trade*, *46*(6), 69-85. In this study, the authors argue that a “static” specification of the Maastricht criterion for long-term bond yields is not conducive to assessing stability of financial systems in euro-candidate countries. They show the stability level of financial systems since the EU’s accession.

● __An empirical study of ____bond ____market transactions__, Hong, G., & Warga, A. (2000). *Financial Analysts Journal*, *56*(2), 32-46. This study presents various bonde market transactions and a comparison on NYSE traded corporate bonds versus dealter-market transactions.

● __Corporate disclosure quality and the cost of debt__, Sengupta, P. (1998). *Accounting review*, 459-474. This paper provides evidence that firms with high disclosure quality ratings from financial analysts enjoy a lower effective interest cost of issuing debt.

● __The role of a corporate ____bond ____market in an economy–and in avoiding crises__, Hakansson, N. (1999). This essay examines the principal differences between an economy with a well-developed corporate bond market free from government interference and an economy in which bank financing plays a central role (as in East Asia).

● __Closed form solutions for term structure derivatives with log____‐____normal ____interest ____rates__, Miltersen, K. R., Sandmann, K., & Sondermann, D. (1997). *The Journal of Finance*, *52*(1), 409-430. The authors wishes to support the crucial assumption that simple interest rates over a fixed finite period are log‐normally distributed for bonds. This assumption is shown to be consistent with the Heath‐Jarrow‐Morton model for a specific choice of volatility.