# MGT338H5 Chapter Notes - Chapter 5: Effective Interest Rate, Annual Percentage Rate, Compound Interest

by OC2183280

Department

ManagementCourse Code

MGT338H5Professor

Gabor ViragChapter

5This

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Chapter 5 – Interest Rates

Chapter 5 – Interest Rates

Effective Annual Rates; Annual Percentage Rates; Converting APR to EAR

→ 5.1: INTEREST RATE QUOTES AND ADJUSTMENTS

The Effective Annual Rate (EAR)

Interest rates are often stated as an effective annual rate (EAR), which indicates the total amount of

interest that will be earned at the end of one year. In Chapters 3 & 4, all interest rates were EARs.

Adjusting the Effective Annual Rate to an Effective Rate Over

Different Time Periods

Imagine an effective annual rate of 5%. A $100,000 investment after 2 years grows to:

This shows that earning an effective annual rate of 5% for two years is equivalent to 10.25% in total

interest over the entire period. In general, by raising the interest rate factor (1 + r) to the appropriate

power, we can compute an equivalent effective interest rate for a longer time period.

We can use the same method to find the equivalent effective interest for periods shorter than one year.

For example, earning a 5% EAR over 6 months is equivalent to receiving:

A 5% EAR is equivalent to an interest rate of approximately 2.47% earned every 6 months; this

would be an effective 6-month rate.

In general, we can convert an effective rate of r for one period to an equivalent effective rate for n

periods using the following formula:

r is the original rate, and to convert it to a new rate you need to set n to the number of current-periods

you want the new period to be made up of. Ex: if r is a 6-month effective rate, and you want the

EAR, n is 2 because there are 2 6-month periods in a year.

Annual Percentage Rates

Banks quote interest rates in terms of an annual percentage rate (APR), which indicates the amount

of simple interest earned in one year. That is, the amount of interest earned without the effect of

compounding even though compounding may occur. Because it does not include the effect of

compounding, the APR is typically less than the actual amount of interest that you will earn. To get

the accurate amount of interest you will, you must convert APR to an EAR.

The APR with k compounding periods is a way of indirectly quoting the effective interest rate, r,

earned each compounding period.

Combining everything we know, we can convert an APR to an EAR by using the following formula:

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