A share has an expected return $()$ of $12\%$ per annum and volatility $()$ of $20\%$

per annum. Changes in the share price satisfy

$dS(t)=S(t)dt+S(t)dW(t).$

$($a$)$ What is the distribution of price increase for the share movement?

$($b$)$ What is the probability that the price of the stock is more than that of the

current price $($i$)$ after $1$ month, $($ii$)$ after $3$ months, $($iii$)$ after $6$ months and

$($iv$)$ after $1$ year. The current price of the stock is $50$ Rs$?$

$($c$)$ What is the probability that the price of the stock will be more than Rs $75$

in two years?