Binary Options

A cash-or-nothing binary call pays a fixed cash amount Q = \100$if$S_T > K$atexpiry,and$0$ otherwise. Given:

$S_0=\$100,K=\$105,r=5\%,T=0.5\text{ years},\sigma =20\%.$

Questions

1. Derive the risk-neutral value of this binary call.
2. Compute the numerical value.
3. How does this relate to the Black-Scholes call formula?