Please show all work so I can learn. Thanks!

For a stock, you are given:

1. The current stock price is 90
2. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%
3. The stocks volatility is 20%
4. You use a three-period forward binomial tree to model the movement of the stock price. The length of each period is 3 months

You are also given that the continuously compounded risk-free rate is 10%

Consider a 9-month 90-strike American put on the stock, calculate the risk-neutral probability that option will be exercised before maturity.

___________________________________

A) 0.1447

B) 0.2756

C) 0.3928

D) 0.5249

E) 0.7244