Sara Sanders purchased $50$ shares of Apple stock at $$190$ per share using the minimum

initial margin requirement of $50\%.$ She held the stock for exactly six months and sold

it without brokerage costs at the end of that period. During the $6-$month holding

period, the stock paid $$1\mathrm{.}46$ per share in cash dividends. Sara was charged $4\mathrm{.}8\%$

annual interest on the margin loan. The minimum maintenance margin was $25\%.$

a$.$ Calculate the initial value of the transaction, the debit balance, and the equity position on Sara$$s transaction.

b$.$ For each of the following share prices, calculate the actual margin percentage, and

indicate whether Sara$$s margin account would have excess equity, would be restricted, or would be subject to a margin call.

$1.$ $$175$

$2.$ $$207$

$3.$ $$122$

c$.$ Calculate the dollar amount of $(1)$ dividends received and $(2)$ interest paid on the

margin loan during the $6-$month holding period.

d$.$ Use each of the following sale prices at the end of the $6-$month holding period to

calculate Sara$$s annualized rate of return on the Apple stock transaction.

$1.$ $$185$

$2.$ $$195$

$3.$ $$207$