A stock was purchased for $51 a share and sold eleven months later for $54 a share. If the shares were purchased totally with cash the holding period return would be percent as compared to percent if the purchase was made using 70 percent margin. Ignore trading costs and margin interest. (Hint: Assume you purchase 10 shares on margin for margin trading case).

5.88%; 8.40%

Explanation:

In finance, the holding period return is simply the return that a portfolio or an asset has accrued during the entire period that the asset or portfolio was being held. It is a way of measuring the performance of an investment.

Based on the information that have been provided in the question,

HPR without margin will be:

= ($54 - $51)/$51

= $3/$51

= 0.588

= 5.88%

HPR with margin will be:

= ($54 - $51)/($51 × 0.70)

= $3/($35.7)

= 0.84

= 8.40%

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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