Additionally, 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 $8\%.$

If the floaters' coupon is set at LIBOR, how is the coupon set on the inverse floaters?

$\frac{3}{4}$ LIBOR $+\frac{1}{4}(x-3**$ LIBOR $)=8\%$

$\frac{3}{4}$ LIBOR $+\frac{1}{4}x-\frac{3}{4}$ LIBOR $=8\%$

$\frac{1}{4}x=8\%$

$x=32\%$

Inverse Floater Coupon is set at $32\%-$ LIBOR

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?

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

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?