The stock of Merton & Black is expected to pay a dividend of $$0\mathrm{.}50$ per share in one month

and $$0\mathrm{.}75$ in four months. The current stock price is $$80,$ and the risk$-$free rate of interest

is $6\%$ per annum with continuous compounding for all maturities. An investor has just

taken a short position in a six$-$month forward contract on the stock.

$$ What is the forward price and the initial value of the forward contract?

$$ Three months later, the price of the stock is $$75$ and the risk$-$free rate of interest is now

$5\%$ per annum. What is the forward price and the value of the short position in the

forward contract?