Emma has half of her investments in a stock paying a 13% dividene and the other half in a stock paying 14% interest. If her total annual return is $540, how much does she have invested?
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I'm sorry, but "uf" does not provide enough context for me to understand what you are asking. Can you please provide more information or rephrase your question?
Let's assume that Emma has x dollars invested in each stock.
As per the given information, half of her investments are in a stock paying a 13% dividend, which means she has (1/2) * x dollars invested in this stock.
The other half of her investments are in a stock paying a 14% interest, which means she also has (1/2) * x dollars invested in this stock.
Now, let's calculate the annual return from each stock:
Annual return from the stock paying a 13% dividend = (13/100) * (1/2) * x = 13x / 200
Annual return from the stock paying a 14% interest = (14/100) * (1/2) * x = 14x / 200
The total annual return is given as $540, so we can write the equation:
13x / 200 + 14x / 200 = 540
Let's solve this equation to find the value of x, which represents the amount invested in each stock.
To solve this problem, we can assign variables to the unknowns. Let's say Emma has x dollars invested in each stock.
According to the problem, Emma has half of her investments in a stock paying a 13% dividend. This means she has 0.5x invested in that stock, and as a result, she earns 0.13 * 0.5x = 0.065x annually from that investment.
Similarly, she has the other half of her investments in a stock paying a 14% interest. Therefore, she earns 0.14 * 0.5x = 0.07x annually from that investment.
The total annual return from both investments combined is given as $540. So, we can equate the sum of the returns from each investment to $540:
0.065x + 0.07x = 540
Combining like terms, we get:
0.135x = 540
Dividing both sides of the equation by 0.135, we can solve for x:
x = 540 / 0.135
x ≈ 4000
Therefore, Emma has a total of $4000 invested (half in each stock).