Duration with semi annual coupon - CFAI mock exam

A bond with a par value of $100 matures in 10 years with a coupon of 4.5% paid semiannually; it is priced to yield 5.83% and has a modified duration of 7.81. If the yield of the bond declines by 0.25%, the approximate percentage price change for the bond is closest to: A. 0.98%. B. 1.95%. C. 3.91%.

The answer’s B ( 7.81*0.25%=1.95%). But i think the discount rate here is YTM/2 so the discount rate just decreases by 0.125%, and the answer may be A. I’m quite confused whether the duratioin measures the percentage of change in price, provided that percentage of change in discount rate or YTM? Because before confronting this problem, i thought that Modified duration is similar with a derivative of a price function with variable of discount rate! Can anybody help me out of this problem? Many thanks!

It measures the % change in price for a change in YTM.

I’d encourage you to calculate the price of the bond at a 5.83% YTM, then calculate the price if the YTM decreases by 0.25%, and compute the percentage price change.

That’s a great idea clarifying my mind a lot. Btw, thank for your help, i really appreciate it!

My pleasure.