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

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4 Feb 2016

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Chapter 6 – Part 2

Annual Percentage Rate

This is the annual rate that is quoted by law

By denition 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?