Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $28, the annual interest rate is 5%, the annual volatility is 25%, and the time to maturity is 6 months. Show the details of your calculations

1. (2 points) What happens to the price of a European call when the volatility increases? What about a European put? Verify your answers by assuming that the volatility goes up to 40%. (Note: We make only one change at a time. The exercise price is still $28.)
2. (2 points) What happens to the price of a European call when the time to maturity is longer? What about a European put? Verify your answers for the time to maturity of 1 year. (Note: We make only one change at a time.)
3. (2 points) What happens to the price of a European call when the interest rate increases? What about a European put? Verify your answers by assuming that the interest rate goes up to 6%. (Note: We make only one change at a time.)