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During the first quarter of 2015, Toronto Dominion Bank (TD) stock cost $45 per share and was expected to yield 4% per year in dividends, while CNA Financial Corp. (CNA) stock cost $40 per share and was expected to yield 2.5% per year in dividends.† If you invested a total of $30,150 in these stocks and expected to earn $936 in dividends in a year, how many shares of each stock did you purchase?

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Answer:

1. The total number of TD stock shares purchases=270

2. The total number of CNA stock shares purchases=450

Explanation:

1. Number of TD stock shares

Step 1: Determine the Total amount invested

Total amount invested=(Cost per TD shareĂ—number of TD shares)+(cost per CNA shareĂ—number of CNA shares)

where;

Total amount invested=$30,150

Cost per TD share=$45

Number of TD shares=x

Cost per CNA share=$40

Number of CNA shares=y

replacing;

45 x+40 y=30,150....equation 1

Step 2: Determine the total dividends in a year

Total dividends=(Expected TD yieldĂ—cost per TD shareĂ—number of TD shares)+(Expected CNA yieldĂ—cost per CNA shareĂ—number of CNA shares)

where;

Total dividends=$936

Expected TD yield=4%=4/100=0.04

Cost per TD share=$45

Number of TD shares=x

Expected CNA yield=2.5%=2.5/100=0.025

Cost per CNA share=$40

Number of CNA shares=y

replacing;

936=(0.04Ă—45Ă—x)+(0.025Ă—40Ă—y)

1.8 x+y=936....equation 2

Step 3:  Combine equation 1 and 2 then solve simultaneously

Multiply equation 1 by 1;

(45 x+40 y=30,150)Ă—1=45 x+40 y=30,150

Multiply equation 2 by 40;

(1.8 x+y=936)Ă—40=72 x+40 y=37,440

Subtract equation 2 from equation 1;

45 x+40 y=30,150

-

72 x+40 y=37,440

-27 x+0=-7,290

-27 x=-7,290

x=-7,290/-27

x=270

The total number of TD stock shares purchases=270

2. Number of CNA stock shares

Replace the value for x in equation 2 above and solve for y;

1.8 x+y=936

where;

x=270

replacing;

(1.8Ă—270)+y=936

486+y=936

y=936-486=450

y=450

The total number of CNA stock shares purchases=450

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