The price of a bond is $$992$ when the effective rate of interest is $4\%.$ The price of the bond decreases to $$973$ when the effective rate of interest increases to $4\mathrm{.}37\%.$ Using the first order Macaulay approximation find the modified duration.

$($A$)5\mathrm{.}45$

$($B$)4\mathrm{.}45$

$($C$)5\mathrm{.}24$

$($D$)4\mathrm{.}24$

$($E$)$ None of the above