Which of the following statements is true?

a$.$ The lower the coupon the lower the bond's duration $($price volatility$)$

b$.$ The longer the maturity the greater the bond's duration $($price volatility$)$

c$.$ The longer the maturity the lower the bond's duration $($price volatility$)$

Consider a $5-$year, $9\%$ coupon bond with a yield to maturity of $8\%$ and a par value of $$100.$ This bond is currently priced at $$104\mathrm{.}05.$ Compute the approximate duration for this bond for a $20bps$ change.

a$.10\mathrm{.}62$

b$.1\mathrm{.}62$

c$.1\mathrm{.}81$

d$.3\mathrm{.}99$