A deposit instrument offered by a bank guarantees that investors will receive a return during a 6-month period that is the greater of (a) zero and (b) $40 \%$ of the return provided by a market index. An investor is planning to put $$\$ 100,000$$ in the instrument. Describe the payoff as an option on the index. Assuming that the risk-free rate of interest is $8 \%$ per annum, the dividend yield on the index is $3 \%$ per annum, and the volatility of the index is $25 \%$ per annum, is the product a good deal for the investor?