forwhat

duration is the first derivative to the interest of the bond pricing.

 

for the zero-coupon bond   BondValue=FaceValue*e^(-r*t)

take the first derivative as BV'(r)=-t*Facevalue*e^(-r*t)=-t*BondValue

therefore, the duration for zero-coupon bond is -t, and usually people ignore the nagetive sign before the number, then duration is t which is the maturity of the bond.