Consider an American put option on a dividend paying stock. The time to maturity is 5 months, the stock price is currently $37. Two dividends are payable: $3.03774 in 1.5 months and $4.11838 in 3.5 months. The strike is $35 and volatility is expected to be 30% p.a. Assume a risk free rate of 10%p.a. Use a 5 step binomial model to price the option. Show all working.