How many Monte Carlo paths for a one-cent price?

You price an at-the-money European call ($S_0 = K = 100$, $r = 5\%$, $\sigma = 20\%$, $T = 1$) by Monte Carlo. A pilot run of 10,000 paths gives a mean discounted payoff of 10.43 and a sample standard deviation of 14.7.

(a) What is the standard error, and what is a 95% confidence interval for the price?

(b) How many paths do you need for the 95% interval to have half-width one cent?

(c) Using the discounted stock price as a control variate, the correlation between the payoff and the control is 0.925. How many paths do you need now?