A stock is expected to pay a dividend of $$0\mathrm{.}6$ per share in $2$ months. The stock price is $$50,$ and the risk$-$free rate of interest is $8\%$ per annum with continuous compounding for all maturities. An investor has just taken a long position in a six$-$month forward contract on the stock.

What is the forward price?

What is the initial value of the forward contract?

Three months later, the price of the stock is $$45$ and the risk$-$free rate of interest is still $8\%$ per annum.

What is the forward price three months later?

What is the value of the long position in the forward contract three months later?

Please do not round during intermediate steps and round your final answer to $2$ decimal places.