For a binomial model for the price of a nondividend-paying stock, you are given:

(i) The length of each period is one month.

(ii) The current stock price is 50.

(iii) u = 1.122401, where u is one plus the percentage change in the stock price per period if the price goes up.

(iv) d = 0.890947, where d is one plus the percentage change in the stock price per period if the price goes down.

(v) The continuously compounded risk-free interest rate is 10%.

Calculate the price of a 3-month 48-strike down-and-out European put option:

(a) With a barrier of 38

(b) With a barrier of 40