What is the difference between Macaulay Duration and Modified Duration?

What is the difference between Macaulay Duration and Modified Duration? 

Ans. The dual use of the word “duration” as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received, and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. When yields are continuously compounded Macaulay duration and modified duration will be numerically equal. When yields are periodically compounded Macaulay and modified duration will differ slightly, and there is a simple relation between the two. Modified duration is used more than Macaulay duration. For bonds with fixed cash flows a price change can come from two sources: 

(i) The passage of time (convergence towards par). This is of course totally predictable, and hence not a risk. 

(ii) A change in the yield. This can be due to a change in the benchmark yield, and/or change in the yield spread.