Question $4-$

$($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 $12M,24M,$ and $36M$ 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 $6M$ and $18M($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?