Consider European and American call options on the same underlying stock.

You are given:

(i) Both options have the same strike price of 100.

(ii) Both options expire in six months.

(iii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 6%.

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

Sketch two separate graphs to show the possible prices of European and American calls against the current stock price S(0). The bounds in your graphs should be as tight as possible. Label the equations of the boundaries and the key points in your graphs clearly.