A $$100$ stock pays a $$1$ dividend every $3$ months with the first dividend coming $2$ months from today. The continuous annual risk free rate is $6\%.$ Suppose you observe a one$-$year forward price on this stock of $$105.$ This forward contract is not correctly priced.

a$)$ Is this contract too expensive or too cheap? Explain.

b$)$ Based on your answer to part a$)$ what arbitrage would you undertake? Demonstrate the arbitrage.