A stock sells for $$30\mathrm{.}00$ per share. You purchase $200$ shares using a $50\%$ margin. A year later, the price has risen to $$45\mathrm{.}00.$ This information is displayed in the following table:

Price Shares Margin

$$30\mathrm{.}0020050\%$

New Price

$$45\mathrm{.}00$

$($a$)$

What is the initial equity you must have to initiate the trade?

You must have an initial equity of $

to initiate the trade.

$($b$)$

What is your percent equity position at the end of the year?

At the end of the year your percent equity position is

$\%.$ Round your answer to $2$ decimal places.