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Question 599891: Cabin Financial Service Group recommends that a client purchase for $10,000 a corporate bond that earns 7% annual simple interest. How much additional money must be placed in U.S. government securities that earn a simple interest rate of 4% so that the total annual interest earned from the two investments is 4.5% of the total investment?
I have tried to set this up in a way that I have used to solve my other problems that are similar to this, but I have been unsuccessful so far.
Answer by Nihal@SriLanka(22)   (Show Source):
You can put this solution on YOUR website! let's assume additional sum invested in government securities is $ x.
Total investment = $ x+10000
Interest on total investment = $ (x+10000) * 4.5/100
Interest on corporate bond = $ 10000 * 7/100 = $ 700
Interest on government securities = $ x * 4/100
Since the interest from both sources should add up to total interest earned
we get the following equation which we proceed to solve
(x+10000) * 4.5/100 = 700 + x * 4/100
Multiplying both sides by 100 we have
(x+10000) * 4.5 = 70000 + x *4
i.e. 4.5x + 45000 = 70000 + 4x
i.e. 4.5x - 4x = 70000 - 45000
i.e. 0.5x = 25000
i.e. x = 25000 * 2
Hence amount to be invested in government securities is $ 50,000.
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