   Chapter 4.3, Problem 20E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Investing: Lesser-Known Stocks Exercises 19 and 20 are based on the following information about the stocks of Whitestone REIT, HCC Insurance Holdings, Inc, and SanDisk Corporation:18 Price ($) Dividend Yield (%) WSR (WSR Whitestone REIT) 16 7 HCC (HCC Insurance Holdings, Inc.) 56 2 SNDK (SanDisk Corporation) 80 2 You invested a total of$11,200 in shares of the three stocks at the given prices and expected to earn $304 in annual dividends. If you purchased a total of 250 shares, how many shares of each stock did you purchase? To determine To calculate: The shares purchased of all three stocks. The price and the dividend yield is given the following table.  Price ($) Dividend Yield (%) WSR (WSR Whitestone REIT) 16 7 HCC (HCC Insurance Holding, Inc.) 56 2 SNDK (SanDisk Corporation) 80 2

It is given that the total investment is $11200, and expected earnings are$304. The total number of shares purchased is 250.

Explanation

Given Information:

The price and the dividend yield is given the following table.

 Price ($) Dividend Yield (%) WSR (WSR Whitestone REIT) 16 7 HCC (HCC Insurance Holding, Inc.) 56 2 SNDK (SanDisk Corporation) 80 2 It is given that the total investment is$11200, and expected earnings are $304. The total number of shares purchased is 250. Formula Used: Elimination method: In this method, we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable. Calculation: Let the stocks purchased of WSR, HCC, and SNDK be x,y,z respectively. The given statement tell that the total investment is$11200.

Investment in share x is at the price of $16, thus 16x. Investment in share y is at the price of$56, thus 56y.

Investment in share z is at the price of $80, thus 80z. Therefore, the total investment can be given by 16x+56y+80z=11200 …… (1) Also, the given statement tell that the expected earning is$304.

Dividend in share x is at the percentage of 7%, thus dividend can be given by 7% of 16x.

Dividend in share y is at the percentage of 2%, thus dividend can be given by 2% of 56y.

Dividend in share z is at the percentage of 2%, thus dividend can be given by 2% of 80z.

Therefore, the total dividend can be given by:

0.07(16)x+0.02(56)y+0.02(80)z=3041.12x+1.12y+1.6z=304 …… (2)

And total stocks purchased are 250.

Thus,

x+y+z=250 …… (3)

Apply the elimination method to find the solution of the given system of the equations:

Multiply equation (3) with 1.6 to eliminate z.

1.6(x+y+z)=1.6(250)1.6x+1.6y+1.6z=400 …… (4)

Now subtract the second equation from fourth to eliminate z.

1.6x+1.6y+1.6z(1.12x+1.12y+1.6z)=400304(1

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