Management and Organizational Studies 2310A/B Lecture Notes - Lecture 10: Special Functions, Effective Interest Rate, Compound Interest

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Chapter 6 – Part 2
Annual Percentage Rate
This is the annual rate that is quoted by law
By denition APR = period rate times the number of periods per
year
Consequently, to get the period rate we rearrange the APR
equation:
oPeriod rate = APR / number of periods per year
You should NEVER divide the e'ective rate by the number of
periods per year – it will NOT give you the period rate
Computing APRs: an example
What is the APR if the monthly rate is .5%?
o.5(12) = 6%
What is the APR if the semi-annual rate is .5%?
o.5(2) = 1%
What is the monthly rate if the APR is 12% with monthly
compounding?
o12 / 12 = 1%
oCan you divide the above APR by 2 to get the semi-annual
rate? NO!!! You need an APR based on semi-annual
compounding to nd the semi-annual rate.
Things to Remember
You ALWAYS need to make sure that the interest rate and the
time period match.
oIf you are looking at annual periods, you need an annual
rate.
oIf you are looking at monthly periods, you need a monthly
rate.
If you have an APR based on monthly compounding, you have to
use monthly periods for lump sums, or adjust the interest rate
appropriately if you have payments other than monthly
Computing APRs from EARs
If you have an e'ective rate, how can you compute the APR?
Rearrange the EAR equation and you get:
oAPR = m [(1+EAR)^1/m – 1]
APR – Example 1
Suppose you want to earn an e'ective rate of 12% and you are
looking at an account that compounds on a monthly basis. What
APR must they pay?
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