A one$-$year long forward contract on a non$-$dividend$-$paying stock is entered into when the stock price is $$50$ and the risk$-$free rate of interest is $8\%$ per annum with continuous compounding.

What are the forward price and the initial value of the forward contract?

Six months later, the price of the stock is $$55$ and the risk$-$free interest rate is still $8\%.$ What are the forward price and the value of the forward contract? Please show all work