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Modified Duration calculations

When converting between modified duration and Macaulay duration, what periodicity should be used for the rates? 

There is a problem in which the annualized Macaulay duration is used, and the YTM is given on a semiannual bond basis, but the modified duration is calculated using (annualized macaulay duration) / (1 + YTM / 2). I do not understand why the semi-annual YTM is used for this calculation, considering that the MacDur has been annualized.

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