Problem $1$ On Jan $1,$ the bid$-$price of XYZ stock is $$79\mathrm{.}9$ and the ask$-$price is $$80\mathrm{.}1.$

Suppose brokerage commission includes $($i$)0\mathrm{.}2\%$ of the transaction amount; plus $($ii$)$ a fixed

cost of $$30$ per transaction.

$($a$)$ If you want to buy $100$ shares of XYZ stock, how much do you need to pay?

$($b$)$ If you sell $100$ shares of XYZ stock, how much will you receive?

On Feb $1,$ the bid$-$price of XYZ stock is $$85\mathrm{.}3$ and the ask$-$price is $$85\mathrm{.}5.$ The conditions of

the brokerage commission remain the same.

$($c$)$ If you sell $100$ shares of XYZ stock on Feb $1$ that you purchased on Jan $1,$ what is the

percentage gain?

$($d$)$ If you had instead purchased $1000$ shares of XYZ stock on Jan $1,$ and now sell all of

them on Feb $1,$ what is the percentage gain?