For a $15-$year, $$1,000$ par value, $7\mathrm{.}45\%$ quarterly pay bond currently trading at $$1,105\mathrm{.}75,$ calculate the approximate

modified duration based on a change in yield of $55$ basis points. How to interpret the result?

A$.9\mathrm{.}5108,$ indicating that the approximate change in price for a $1\%$ change in yield to maturity $($YTM$)$ is $9\mathrm{.}5108\%.$

B$.9\mathrm{.}3221,$ indicating that the approximate change in price for a $1\%$ change in yield to maturity $($YTM$)$ is $9\mathrm{.}3221\%.$

C$.8\mathrm{.}9915,$ indicating that the approximate change in price for a $1\%$ change in yield to maturity $($YTM$)$ is $8\mathrm{.}9915\%.$

D$.8\mathrm{.}5094,$ indicating that the approximate change in price for a $1\%$ change in yield to maturity $($YTM$)$ is $8\mathrm{.}5094\%.$