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# Equivalent Annual Rate

I have a discussion that deals with exercises in determining Equivalent Annual Rate (EAR.) This is closely related to the time value of money and deals with how the frequency of compounding of the interest rate affects the value calculation. The result is not the same when interest is compounded quarterly, for example, as it is when interest is compounded annually.

Most of the time in finance we deal with things on an annual basis. For this reason, it is important to be able to adjust the interest rate from daily, weekly, or monthly compounding to the EAR as if the interest were being compounded annually.

I need help on this practice question: A while back, my credit union sent me a statement in which they listed the "Dividend rate" and the "Compounding Term for securities they offer. Some are:

Regular Share Account: 1.24% monthly

Six-month Money Market Certificate: 3.96% Semiannually

One-year Money Market Certificate: 4.21% Daily

Question: What are EARs for each of the above?

#### Solution Preview

The formula to find the effective annual rate is:

Effective annual rate = ((1+rate per compounding period)^number of compounding periods) - 1

Thus,

Regular Share Account: 1.24% monthly

Effective annual rate = ((1+rate per compounding period)^number of ...

#### Solution Summary

This solution illustrates how to compare financial instruments bearing different nominal interest rates for different compounding periods by computing each one's equivalent annual rate.

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