(12C) Annualised Equivalent Rate & Continuously Compounded Rate

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An extract from:
Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition By Andrew M. Chisholm © 2010 John Wiley & Sons, Ltd.

page 217
The … annual equivalent rate (AER) or the effective annual rate … measures the rate expressed with annual compounding that is equivalent to a rate expressed with interest compounded at more frequent intervals, such as twice a year. For example, a rate of 10% p.a. with semi-annual compounding is equivalent to 10.25% p.a. expressed with annual compounding (i.e. the AER is 10.25% p.a.).

page 218
AER formula
The formula for calculating the AER when interest is compounded m times per annum is as follows:
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For example, a nominal rate of 10% p.a. with semi-annual compounding is equivalent to 10.25% p.a. with annual compounding.
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