please answer the following questions about CMOs. For questions $8-11,$ assume there exists a tranche of a CMO with a total principle value of $$80,000,000.$ This tranche is divided into $$60,000,000$ of floaters and $$20,000,000$ of inverse floaters. The pool is at a fixed rate of $8\%.$

$8)$ If the floaters$$ coupon is set at LIBOR, how is the coupon set on the inverse floaters?

$9)$ How does the duration of the inverse floater compare with the duration of an $8\%$ fixed rate note of comparable maturity to the mortgage pool?

$10)$ At what rate is LIBOR implicitly capped based on you answer to $(1)?$

$11)$ If the duration of the underlying mortgage pool is $6$ years and an investor were to lever up their position in the inverse floater by $2\mathrm{.}5-$to$-1,$ what would be the duration of their position?