A non-dividend paying stock costs $50. Analysts estimate that there is a 50% chance that the stock trades for $60 next year if the company suceeds in developping an important vaccine. Otherwise, the stock could fall to $40. The risk-free rate is 5% per year with continuous compounding. What should be the price of a security that pays $100 next year if the stock goes up, and $0 otherwise?

Group of answer choices

47.56

50

59.75

62.82