$($a$)$ Consider a $3-$year forward contract to buy a coupon$-$bearing bond that will mature $3-$years from today. The current price of the bond is $$120.$ Suppose that on that bond $3$ coupon payments of $$10$ are expected after $12,24,$ and $36$ months. We assume that the $12$M$,24$M$,$ and $36$M risk$-$free interest rates $($continuously compounded$)$ are $1\mathrm{.}75\%,$ $$2\mathrm{.}1,$ and $2\mathrm{.}5\%$ per annum, respectively. Determine the strike price, the forward price and the value of the forward contract.

$($b$)18$ months later, the price of the bond is $$105$ and the risk$-$free interest rates for maturity $6$M and $18$M $($continuously compounded$)$ are $1\mathrm{.}1\%$ and $1\mathrm{.}9\%$ per annum, respectively. What are the strike price, the forward price and the value of the forward contract?