Suppose a bond is purchased with a settlement date of October $15$ and the next coupon payment is on December $1.$ The par amount purchased on the bond is $$100,000$ and its semiannual coupon rate is $4\%.$ What is the accrued interest using the actual$/$actual day$-$count convention?

$$2\mathrm{.}95$ per $$100$

$$2\mathrm{.}97$ per $$100$

$$3\mathrm{.}03$ per $$100$

$$2\mathrm{.}89$ per $$100$