Please do all parts.

Problem 1 (2 points): It may be intuitive that more 1 frequent compounding yields higher returns. Mathematically speaking, show why a semi-annual compounding at a rate of r yields a higher return than an annual compounding at the same rate of r. Problem 2 (4 points): Assume Asset A costs $40 today, and that the risk-free, continuously compounded interest rate is 6%. What is the arbitrage opportunity for a 1-year forward contract for the below two scenarios? Show your work 1. 1Y Forward Price = $45 today 2. 1Y Forward Price = $35 today = Problem 3 (4 points): A $50 stock pays an 8% continuous dividend. The continuously compounded risk-free rate is 6%. 1. What is the price of a prepaid forward contract that expires 1 year from today? 2. What is the price of a forward contract that expires at the same time