Question $2$: Interest Rate Forwards $(2/10)$ Suppose on Jan $1,$ your new firm wants

to borrow $$1$M in $6$ months $($on Jul $1)$ and pays back in $12$ months $($on Dec $31).$ The interest

rates $($simple$,$ annual$)$ are: r$0,6=4\%$ from now $($Jan $1)$ to $6$ months $($Jul $1),$ and r$0,12=5\%$

from now $($Jan $1)$ to $12$ months $($Dec $31).$

$($i$)$ What is a fair forward rate from $6$ months to $12$ months f$0,6,12($simple$,$ annual$)$ today?

$($ii$)$ Suppose you want to use Forward Rate Agreement $($FRA$)$ to make sure you borrow

money at a pre$-$specified rate in $6$ months, what should you do$?$

$($iii$)$ Suppose after $6$ months on Jul $1,$ the interest rate $($simple annual$)$ is r$6,12=7\%$ from

Jul $1$ to Dec $31.$ What is your FRA settlement on Jul $1?$

$($iv$)$ Following $($iii$),$ what are your detailed cash flows on Jan $1,$ Jul $1$ and Dec $31?$