A stock is expected to pay a dividend of $1 per share in three months and another dividend of $1 per share in nine months. The stock price is $50 today, and the risk-free rate of interest is 5% per annum with continuous compounding for all maturities. Today, an investor takes a long position in a one-year forward contract on the stock.

Today, what are the forward price and the initial value of the forward contract?

Five months from today, assume that the price of the stock will be $55 and that the risk-free rate of interest will still be 5% per annum. What will be the forward price and the value of the long position in the forward contract written at the initial price determined in a)?