Compute the followings. $($showing each step of calculation is a must$)$:$($a$)$ How much does a deposit of Rs$\mathrm{.}40000$ grow at the end of $10$ years at the rate of $6$ per cent interest and compounding is done semi$-$annually.

$($b$)$ A finance company advertises that it will pay a lump sum of Rs$.44650$ at the end of five years to investors who deposit annually Rs$.6000$ for $5$ years. What is the interest rate implicit in this offer?

$($c$)$ Sneha borrows Rs$.100000$ for her new business at a monthly interest of $1\mathrm{.}25$ per cent. The loan is to be repaid in $12$ equal monthly installments, payable at the end of each month. What is the monthly installment amount?

$($d$)$ A stock with holding period of three years has the following estimated dividend payments: Year $1=$ Rs$.1\mathrm{.}10$; Year $2=$ Rs$.1\mathrm{.}25$ and Year $3=$Rs$.1\mathrm{.}50.$ The estimated sale price of Rs$\mathrm{.}57,$ three years from now. Required rate of return is $15\%.$ What is the present value of this stock?