# Initial margin requirement as percentage, not dollar value

Problem from Finan, FM/2

On 12-30-1998, you decided to bet on the January effect. ON that day, you bought 400 shares of Microsoft on margin at the price of 139 per share. The initial margin requirement is 55% and the maintenance margin is 30%. The annual cost of the margin loan is 6.5%

To what price must Microsoft fall for you to receive a margin call?

So if we use the Initial margin requirement formula $$IM=P\cdot{Q}\cdot{IM\text{%}}$$

But the correct answer of 89.36 as Microsoft price is given only if $\text{IM%}$ is 45%. Does this mean that we use $1-IM\text{%}%$ as the initial margin percentage? I'm confused about the wording because the problem gives you initial margin requirement as a percentage and not as a dollar value. If you put 55% in the above equation you do not get the right answer. No where in the texts that I'm using does it state initial margin requirement as a percentage is $1-IM\text{%}$?

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so then calculating the price, we do $$\frac{400\cdot{X}-400\cdot{139}\cdot{.45}}{400\cdot{X}}=.3$$ Solving for X gives us \$89.36.