A stock is expected to pay a dividend of $$1\mathrm{.}0$ per share in $3$ months and a dividend of $$1\mathrm{.}5$ per share in $6$ months. The current stock price is $$121,$ and the risk$-$free rate of interest is $7\%$ per annum with continuous compounding for all maturities. An investor has just taken a short position in an $8-$month forward contract on the stock.

a$.$ What are the forward price and the initial value of the forward contract?

b$.$ Four months later, the price of the stock is $$125$ and the risk$-$free rate of interest drops to $5\mathrm{.}5\%$ per annum with continuous compounding for all maturities. What are the forward price and the value of the short position in the forward contract?