Consider a two$-$period binomial model in which a stock currently trades at a price of K$65.$ The stock price can go up $20$ percent or down $17$ percent each period. The risk$-$free rate is $5$ percent.

$($i$)$Calculate the price of a put option expiring in two periods with an exercise price of K$60.$

$($ii$)$Calculate the price of a call option expiring in two periods with an exercise price of K$70.$