You need to price a put option on the stock of APPLE with an exercise price of $50 and six months to expiration. The current stock price of APPLE is $52, the risk-free rate is 10% p.a. (c.c.) and the volatility of the stock price of APPLE is 30% p.a. APPLE will pay a dividend of $1 in exactly four months time. This put option is to be priced using a two-period binomial option pricing model, with three months in each period.

QUESTION: Compare an American put option with an otherwise identical European put option on the stock of APPLE. What is the value of the right to exercise the put option before expiry?

Provide workings and calculations.