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Homework answers / question archive / The following question is based on the following information about the stocks of KT Corporation, International Flavors & Fragrances, and Quality Systems
The following question is based on the following information about the stocks of KT Corporation, International Flavors & Fragrances, and Quality Systems. Price Dividend Yield KT (KT Corporation) $16 7% IFF (International $56 2% Flavors & Fragrances) QSII (Quality Systems) $80 2% You invested a total of $14,400 in shares of the three stocks at the given prices, and expected to earn $328 in annual dividends. If you purchased a total of 250 shares, how many shares of each stock did you purchase? KT shares IFF shares QSII shares
Let X be the number of shares brought of KT
Y be the number of shares of IFF
Z be the number of shares of QSII
Now Given that the total shares brought is 250
X + Y + Z = 250 -------------Equation -1
Amount invested is 14,400
That means
16X + 56Y + 80Z = 14,400----------------Equation -2
Given that the dividends earned is 328
That means
0.07*16X + 0.02*56Y +0.02*80Z = 328-----------Equation-3
Now, we will solve these 3 equations as follows.
Form Euqation -1
X = 250-Y -Z
We will substitute this in equation 2 and 3 then we get
In equation-2
16(250-Y-Z) + 56Y + 80Z = 14,400
= 4000 - 16Y -16Z + 56Y + 80Z = 14,400
40Y + 64Z = 10400
= 5Y + 8Z = 1300 ------------Equation ---4
In equation-3
0.07*16(250-Y -Z) + 0.02*56Y +0.02*80Z = 328
1.12(250-Y-Z) + 1.12Y + 1.6Z = 328
280 - 1.12Y - 1.12Z + 1.12Y +1.6Z = 328
0.48Z = 328-280
Z = 48/0.48 = 100 Shares
Now, we will substitute this equation 4 and get
5Y + 800 = 1300
5Y = 500
Y = 100
We have X + Y + Z = 250
X = 250 -200
X = 50
Hence X = 50 and Y = Z = 100
