A stock is expected to pay a dividend of $$1$ per share in two months and in five months. The stock price is $$56,$ and the risk$-$free rate $($with continuous compounding$)$ is $8\%$ for all maturities. An investor has just taken a short position in a seven$-$month forward contract on the stock.$`$

$(1)$ What are the forward price and the initial value of the forward contract?

$(2)$ Three months later, the price of the stock is $$50$ and the risk$-$free rate is still $8\%.$ What are the forward price and the value of the forward contract?