SOLUTION: an investment manager bought a bond of a pharmaceutical company for 5000. The bond yield 4% per year. The manager now wants to buy shares of stock in telecommunication company. The
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Question 1201493: an investment manager bought a bond of a pharmaceutical company for 5000. The bond yield 4% per year. The manager now wants to buy shares of stock in telecommunication company. The stock sells at $20 perper share and earn a dividend of 0,50 per share per year. How many share should the manager buy so that its yield from the total investment in stocks and bonds higher than 3% per year ? Found 3 solutions by mananth, greenestamps, ikleyn:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! a bond of a pharmaceutical company for 5000.
The bond yield 4% per year
Dividend = 200
. The stock sells at $20 per share
and earn a dividend of 0,50 per share per year.
Let x be the number of shares he has to buy
The value of shares to be purchased = 20x
20x +5000 should fetch him 3 % or more
Interest to be earned 3%(20x+5000)
2.5% 20x +4% 5000 = 3%(20x+5000)
2.5*20x +20000= 60x +15000
10x =5000
x=500
More than 500 shares
Investment in shares =500*20 10000
Dividend on shares = 2.5% = 250
Interest on bonds = 200
Total income = 450 on investment of 15000 =3 %
Here is a quick and easy informal method for solving any 2-part "mixture" problem like this.
The yield from the bond is 4%.
The yield on the stock is 0.5/20 = 2.5%.
The desired (minimum) overall yield is 3%.
3% is "twice as close" to 2.5% as it is to 4%.
That means the overall yield of 3% is achieved when the amount of the investment in the stock is twice the amount of the investment in the bond.
Since the amount of the investment in the bond was $5000, the amount of the investment in the stock should be $10,000.
Since the stock sells at $20 per share, the number of shares to purchase to achieve on overall yield of 3% is 10000/20 = 500.
ANSWER: 500 shares
NOTE: The problem is not well stated. Buying 500 shares of the stock will result in an overall yield of EXACTLY 3%. The answer that is asked for is the number of shares to buy to make the overall yield HIGHER THAN 3%. The answer to that question is any number of shares LESS THAN 500.
