the maintenance margin is $25\%.$ The annual interest rate on margin loan is $5\%$ and brokerage cost is $1\%$ of value of stocks purchased.

Value of stocks purchased $=$$$503000=$$$150,000$

Brokerage cost $=$$$1500000\mathrm{.}01=$$$1500$

Total costs $=$$$150,000+$$$1500=$$$151,500$

Margin requirement $($initial margin$)=$$$151,5000\mathrm{.}6=$$$90,900$ this is the amount of cash you must put up $$ your equity

Amount borrowed $=$$$151,500-$$$90,900=$$$60,600$

Assume that the price of the stock declines immediately. Interest that you would owe for an hour or two is very negligible. For practical reason, let us assume that it is $$0.$ How far the stock price $($P$)$ has to fall immediately for you to get a margin call? If the stock price is $P($critical price$),$

$E=3000xP-$$$60,600$

Maintenance margin $=\frac{E}{?}$ Market value of stocks bought

$0\mathrm{.}25=\frac{3000P-\text{\$}60,600}{P3000}$

$0\mathrm{.}25(P3000)=3000P-$$$60,600$

$750P=3000P-$$$60,600$

$$60,600=3000P-750P$

$P=$$$60,\frac{600}{2250}=$$$26\mathrm{.}93$

If the stock price declines to $$26\mathrm{.}93$ or lower, you will get a margin call. Critical price $=$$$26\mathrm{.}93$

Homework: Now assume that six months have passed since your purchase.

What would be the critical price to get a margin call? $$27\mathrm{.}61$