For all problems where a risk free rate or a dividend yield is given, assume that the interest rate and the dividend yield are annual and continuously compounded rates.

A stock index futures price is currently $3100, the dividend yield on the index is 2% per year, and the risk-free interest rate is 4% per year for all maturities. The maturity of the futures contract is 1 year. What is a lower bound for the price of a 6-month European put option on the index futures when the strike price is $3300? What is a lower bound for the price of a 6-month European put option on the index spot price when the strike price is $3300?