Forecasting return blue box - Duration calculation - Economics

This is for blue box 1 of reading 4. I understand what is happening and how they compare reinvestment impact to capital gains/losses impact with an increase in yields but why do we use macaulay duration instead of modified duration?

They solve for Macaulay duration but could I just compare to Modified?

I think because Macauley duration is a true measure of time while modified duration is a sensitivity measure. In the exercise one should compare the investment horizon (in years) with the duration of the bonds portfolio (in years). To do that, the appropriate measure of time is the Macualay duration, by definition. Actually Macduration and Mod duration would be the same thing in case of yields continously compounding.