$(4)$ Consider a three months ATM call with strike $40$ on an underlying asset with spot price $40$

following a lognormal distribution with volatility $20\%$ and paying dividends continuously at

$1\%.$ Assume the risk$$free interest rate is constant at $5\%.$

$($i$)$ Compute the Black$$Scholes value of the call using the routine from Table $3\mathrm{.}1$ for com$-$

puting approximate values for cumulative distributions of the standard normal variable;

$($ii$)$ Compute the Black$$Scholes value of the call using Simpson$$s rule with tolerance $1012$

to compute approximate values for cumulative distributions of the standard normal variable.