A$.)$ Suppose that a floating$-$rate security is currently trading at its par value of $$1,000.$ The security has $10$ annual coupon payments remaining. Coupon payments are based on a reference rate plus a spread of $2\%.$ There is also a coupon rate cap $($ceiling$)$ of $7\%.$ Suppose that the reference rate is currently $3\%$ but increases to $4\mathrm{.}5\%$ next year. Based on the information provided, what is the most probable price of this floater next year?

B$.)$ A semiannual bond is purchased between coupon periods. The days between the settlement $($sale$)$ date and the next coupon period are $100.$ There are $180$ days in the coupon period. Suppose that the bond purchased has a coupon rate of $5\%$ and there are $20$ semiannual coupon payments remaining. The required yield is $6\%.$ Calculate the full $($dirty$)$ price.

C$.)$ Based on the information in the previous problem, calculate the accrued interest.

D$.)$ Based on the information in questions #$8$ and #$9,$ calculate the clean price.