Effective Rate

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Chapter 9 Personal Finance
9.4
Effective Rate of Interest
9.4.1
MATHPOWERTM 11, WESTERN EDITION
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The Effective Annual Rate
The Nominal Interest Rate is the stated or named
rate of interest of an investment or a loan. This
is usually a compounded rate.
The Effective Annual Rate is the simple interest
rate that would produce the same interest as the
nominal interest rate.
An investment pays interest at 8
compounded semi-annually. What is the effective
annual interest rate?
Find the accumulated amount of 1 in one year
Therefore the Effective Annual Rate of interest
is 8.16.
Find the amount of interest 1.0816 - 1 0.0816
A P(1 i)n A 1(1 0.04)2 A 1.0816
9.4.2
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Applying The Effective Annual Rate
You can use the effective annual interest rate to
decide which interest option might be better.
Option A 8.30 compounded quarterly Option B
8.35 compounded semi-annually
Option B
Option A
Interest 8.35 2 4.175
Interest 8.30 4 2.075
A P(1 i)n 1(1 0.04175)2 1.0852
A P(1 i)n 1(1 .02075)4 1.0856
Therefore, the effective annual rate of
interest is 1.0852 - 1 0.0852
8.52.
Therefore, the effective annual rate of
interest is 1.0856 - 1 0.0856
8.56.
9.4.3
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Assignment
Suggested Questions
Page 549 1-3, 4-15 even
9.4.4