The current price of a stock is $305 and the annual standard deviation of the rate of return on the stock is 50%. The stock is expected to pay dividends of $5 in 1 months and $5 in 4 months.

A European call option on the stock has a strike price of $320 and expires in 0.5 years. The risk-free rate is 7% (continuously compounded).

a. What should be the price (premium) of the European call option?

b. What should be the price (premium) of the American call option according to Black's approximation?