The current price of a non-dividend-paying stock is $40. Over each of the next two 90-day periods it is expected to rise by 5% or fall by 7.5%. European and American options on the stock have a strike price of $41 and an expiration date in 180 days. The risk-free interest rate is 2% per annum with continuous compounding. Use 365 days in a year. What is the value of each American put option ?

a. $1.53

b. $1.46

c. $1.93