give all 3 solution with steps please

1. An exchange rate is currently $5.00. The volatility of the exchange rate is quoted as 20% and interest rates in the two countries are the same. Using the Black Scholes model for foreign currencies, estimate the probabilities that the exchange rate in one year will be (a) less than or equal to $4.50, (b) between $4.50 and $5.50, and (c) greater than $5.50.

2. Compute the probability that the S&P 500 index is greater than 2,300 in 6 months according to the Black Scholes model. Assume that the current level of the index is 2,200, the risk-free rate is 1% per annum, the dividend yield on the index is 2% per annum, and the volatility of the index is 25%.

3. For a European call option on a currency, the exchange rate is $1.0000, the strike price is $0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. How low can the option price be without there being an arbitrage opportunity?