An investment adviser invested $14,000 in two accounts. One investment earned 7% annual simple interest, and the other investment earned 5.5% annual simple interest. The amount of interest earned for 1 year was $884. How much was invested in each account?
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find the simple interest on rs 6000 from 16 may 2010 to 9 october 2010 at 10% per annum
Let's assume the amount invested at 7% interest is represented by x, and the amount invested at 5.5% interest is represented by y.
According to the information given, the total amount invested is $14,000. So, we know that:
x + y = $14,000 ---(1)
The interest earned from the investment at 7% interest is calculated using the formula I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years. In this case, P = x, r = 7%, and t = 1 year. So, the interest earned from the investment at 7% interest is:
0.07x
Similarly, the interest earned from the investment at 5.5% interest is:
0.055y
According to the information given, the total interest earned for 1 year is $884. So, we have another equation:
0.07x + 0.055y = $884 ---(2)
Now, we can solve these two equations (1) and (2) simultaneously to find the values of x and y.
To solve this problem, we can use a system of equations. Let's assume that the amount invested in the account earning 7% annual simple interest is x dollars. Therefore, the amount invested in the account earning 5.5% annual simple interest would be (14000 - x) dollars.
Now, let's calculate the interest earned for one year on these investments. The interest earned from the account earning 7% is given by 0.07x, and the interest earned from the account earning 5.5% is given by 0.055(14000 - x). According to the problem, the total interest earned for one year is $884. Therefore, we can set up the equation:
0.07x + 0.055(14000 - x) = 884
Next, let's solve this equation to find the value of x.
0.07x + 0.055(14000 - x) = 884
0.07x + 770 - 0.055x = 884
0.015x + 770 = 884
0.015x = 114
x = 114 / 0.015
x ≈ 7600
So, approximately $7600 was invested in the account earning 7% annual simple interest. Since the total amount invested is $14000, the remaining amount would be $14000 - $7600 = $6400. Therefore, $6400 was invested in the account earning 5.5% annual simple interest.
In summary, $7600 was invested in the account earning 7% annual simple interest, and $6400 was invested in the account earning 5.5% annual simple interest.