The Hang Seng Index of the Hong Kong Stock Exchange has just closed at 20,295 and its volatility is expected to be 25% p.a. over the coming year. The dividend yield on the index is 3% p.a. and the risk-free interest rate is 5% p.a continuously compounded. You are asked to value a derivative written on the index, that pays off $600 in four months from today if the index is higher than 21,000 at that date and zero otherwise. The derivative asset is European-style. Use a two-step tree to calculate the value of the derivative.

For all calculations, round to 4 decimal digits at each step. Please show all your workings.