Problem $1$

A stock is expected to pay a dividend of $$1$ per share in two months and five months. The stock price is $$50,$

and the risk$-$free rate of interest is $8\%$ per annum with continuous compounding for all maturities. An

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

What is the present value of the income from the security?

What is the forward price of the forward contract?

What is the initial value of the forward contract?

Three months later, the price of the stock s $$48$ and the risk$-$free rate of interest is still $8\%$ per annum.

What is the present value of the income from the security now?

What is the forward price of the forward contract now?

What is the value of the forward contract now?