$(10\text{'})$ Suppose a bond is purchased with a settlement date of June $30$ and the next coupon payment is on September $30.$ The par amount purchased on the bond $$100,000,$ and its annual coupon rate is $6\%$ paid semiannually.

a$.$ What is the accrued interest using the $\frac{30}{360}$ day count convention?

b$.$ What is the accrued interest using the actual$/$actual day count convention