lunarfollies

The book is correct. Taking the (1/nth ) root gives you the CAGR. For example, if you have $100 and it grows by 10% to $110 in year one and 10% again in year two to $121, your HPY is (1+10%)*(1+10%)-1 = 21%, which is correct. Since (121-100)/100 = 21%

If you take ((1+10%)*(1+10%))^.5-1, that gives you 10% which is just the CAGR.

I answered my own question. Hope it helped clarify this for others who were wondering as well.