Suppose that a stock price has an expected return of $2\mathrm{.}5\%$ per annum and a volatility of $15\%$ per annum. When the stock price at the end of a certain day is $$60,$ calculate each of the following:

$($i$)$ The expected stock price $15$ days later;

$($ii$)$ The standard deviation of the stock price $15$ days later;

$($iii$)$ The $95\%$ confidence interval for the stock price $15$ days later.