$(6)$ Consider a five months European call option with strike $45$ on an underlying asset with spot

price $50,$ following a lognormal distribution with drift $3\%$ and volatility $30\%,$ and paying

$1\%$ dividends continuously. Assume that the risk$$free rate is constant at $3\%.$

$($i$)$ Compute and explain the difference between N$($d$1)$ and the Delta of the option;

$($ii$)$ Compute and explain the difference between N$($d$2)$ and the probability that the call

option expires in the money.