A bond issued by Hang Seng Bank some time ago worked as follows. The interest that the buyer received was not fixed. At the bond's maturity the bank promised to pay $1,000 plus an additional amount based on the performance of Hang Seng Index at that time. The additional amount was equal to the product of 0.1 and the excess (if any) of the index value at the maturity over 27,000. The maximum additional amount paid was capped at $200. Please propose a formula based on the Black-Scholes option pricing equation to evaluate such bond. Show your analysis process