price of a European call option

Use the following inputs to compute the price of a European call option: S = $50, K = $100, r = 0.06, s = 0.30, T = 0.01, d = 0.
a. Verify that the Black-Scholes price is zero.
b. Verify that the vega for this option is zero. Why is this so?
c. Suppose you observe a bid price of zero and an ask price of $0.05. What answers do you obtain when you compute implied volatility for these prices. Why?
d. Why would market-makers set such prices?
e. What can you conclude about difficulties in computing and interpreting implied volatility for very short-term, deep out-of-the-money options?