$($i$)$ A forward contract written on a bond has $10$ months remaining until maturity.

The face value of the bond is $$1000,$ and it pays a $7\%$ coupon every $6$ months.

The final coupon is due immediately prior to the maturity of the forward. The relevant riskless rate of interest is $5\%.$

If the bond is trading at $$1025,$

calculate the theoretical forward price and initial value

of the forward contract and explain the forward pricing relationship.

Provide numerical examples of arbitrage strategies for situations where a broker offers a

price above, and below the theoretical forward price.