An investor has just taken a short position in a one$-$year forward contract on a dividend paying stock. The stock is expected to pay a dividend of $$4$ per share in five months and in eleven months. The stock price is currently selling for $$100$ and the risk$-$free rate of interest is $7\%$ per year with continuous compounding for all maturities.

a$.$ What are the forward price $($F$0=($S$0-$I$)$erT$)$ and the initial value of the forward contract? The forward price is $94\mathrm{.}005($sample answer: $75\mathrm{.}50)$ and the initial value is $0($sample answer: $75\mathrm{.}50)$

b$.$Six months later, the price of the stock is $$105$ and the risk$-$free rate stays the same. What are the forward price $($F$0=($S$0-$I$)$erT$)$ and the value of the position in the forward contract? Now the forward price is $99\mathrm{.}132($sample answer: $75\mathrm{.}50)$ and the value of the forward position is $5\mathrm{.}127($sample answer: $+5\mathrm{.}50$; or $-5\mathrm{.}50)$