A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 5% or down by 5%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a six-month Americanputoption with a strike price of $50?

*Equations you may find helpful:

p = (e^(rt)-d) / (u-d)

f = e^(-rt) * (fu*p + fd*(1-p))

(required precision 0.01 +/- 0.01)