A total of 10,000 is invested into two funds paying 7.5% and 9% simple interest. The combined annual income for the two funds is $849. Determine how much is invested at each rate
To determine how much is invested at each rate, we can use a system of equations. Let's assume the amount invested at 7.5% is x dollars, and the amount invested at 9% is y dollars.
Given:
Total investment = $10,000
Combined annual income = $849
We know that the interest earned on the amount invested at 7.5% is given by `(x * 7.5%) / 100` and the interest earned on the amount invested at 9% is given by `(y * 9%) / 100`.
According to the given problem, the sum of these two interests is equal to $849:
`(x * 7.5%) / 100 + (y * 9%) / 100 = $849`
We also know that the sum of the amounts invested at each rate should equal the total investment:
x + y = $10,000
Now, we have a system of two equations:
1) `(x * 7.5%) / 100 + (y * 9%) / 100 = $849`
2) x + y = $10,000
To solve this system of equations, we can use the substitution or elimination method.
Let's solve it using the substitution method:
From equation 2), we have x = $10,000 - y.
Substitute this value of x into equation 1):
`((10,000 - y) * 7.5%) / 100 + (y * 9%) / 100 = $849`
Simplifying the equation:
`(750,000 - 7,500y + 900y) / 100 = $849`
`(150y + 750,000) / 100 = $849`
150y + 750,000 = $84,900
150y = $84,900 - $750,000
150y = -$665,100
y = -$665,100 / 150
y = -$4,434
This means that y = -$4,434, which does not make sense as we can't have a negative investment amount. It seems there may be an error or inconsistency in the given information.
Please double-check the values or provide any additional information if available.
If $x is at 7.5%, then the rest (10000-x) is at 9%. So, add up the interest:
.075x + .09(10000-x) = 849
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