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Effective Interest Rate or Yield

Moneyzine Editor
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Moneyzine Editor
2 mins
January 16th, 2024
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Effective Interest Rate or Yield

Definition

The term effective interest rate is used to describe the actual rate of interest received when compounding is applied to a nominal rate of interest. The effective interest rate is useful when evaluating alternatives involving various nominal rates applied to different compounding periods.

Calculation

Effective Interest Rate = (1 + Rate / N)N x T - 1

Where:

  • N = number of times the rate is compounded each time period

  • T = total number of time periods

  • R = rate expressed in decimal form

Explanation

Also known as effective yield and effective annual interest rate, this is a measure of the rate of interest earned on a loan, or bank deposit, when compounding is applied to the nominal (stated) interest rate.

Compounding takes an interest rate and applies it multiple times in the same period. In doing so, it applies the interest rate to both the principal as well as the growth in principal. When compounding is applied, the effective rate of interest paid will always be higher than the nominal rate applied.

The annual interest rate is useful when comparing loans that offer differing compounding periods (for example, semi-annual, quarterly, and monthly) in addition to differing nominal rates. The effective interest rate should not be confused with the legal term Annual Percentage Rate, which also takes into consideration fees and other costs associated with a loan.

This website offers a compound interest calculator that applies the above concepts to nominal interest rates, and provides semi-annual, quarterly, monthly, weekly and daily results.

Example

Lindsey is comparing two offers from local banks. First Federal is offering an annual interest rate of 7.20%, while Second National Bank is offering a rate of 7.00% with daily compounding. To make a fair comparison, the Second National Bank needs to be converted into an effective yield.

= (1 + 0.07 / 365)365 - 1 = (1 + 0.000192)365 - 1 = (1.000192)365 - 1 = 1.07250 - 1, or 0.0725

The effective annual interest rate offered by Second National Bank is 0.0725 or 7.25%, which is higher than the offer from First Federal of 7.20%.

Related Terms

  • The term simple interest is used to describe a calculation involving the application of a rate to principal. Simple interest would be equal to the financing charge associated with the outstanding principal of a loan in one period of time.
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  • Compound Interest
    The term compound interest is used to describe a calculation involving the application of a rate to both principal and interest that has been earned, but not yet paid or withdrawn. Compound interest would be equal to the growth of principal for two or more periods, if that growth is added back to the principal at the end of each period of time.
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  • The true cost of a loan is measured by the annual percentage rate, or APR. This is the annualized cost of a loan, which not only takes into consideration the interest charges on the loan's principal, but also application fees, points, and insurance.
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  • Future Value
    The term future value is used to describe the worth of an asset at a later time. Future value is a nominal sum of money received in the future, assuming a given rate of interest earned.
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  • The term principal can have several meanings. It can refer to the remaining balance on a mortgage or loan, the owner of a privately owned company, or even the par value of a bond. When the term principal is used in this publication, it's often referencing the outstanding balance on a loan.
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