A total of 23,456.78 dollars was invested in two funds paying 2½ percent and 1¾ annual interest. The combined interest for the year percent is 368 dollars and 50 cents.
Part A: How much of the 23,456.78 dollars is invested in 2½ percent fund?
Part B: How much of the 23,456.78 dollars is invested in 1¾ percent fund?
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To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the amount invested in the 2½ percent fund is x dollars. This means that the amount invested in the 1¾ percent fund will be (23,456.78 - x) dollars.
Part A: How much of the 23,456.78 dollars is invested in the 2½ percent fund?
The formula to calculate the interest earned from an investment is:
Interest = Principal * Rate * Time
For the 2½ percent fund, the interest earned can be calculated as:
Interest1 = x * 0.025 * 1
Part B: How much of the 23,456.78 dollars is invested in the 1¾ percent fund?
For the 1¾ percent fund, the interest earned can be calculated as:
Interest2 = (23,456.78 - x) * 0.0175 * 1
We also know that the combined interest earned for the year is 368 dollars and 50 cents:
Interest1 + Interest2 = 368.50
Now we can set up an equation using the above information and solve for x:
x * 0.025 * 1 + (23,456.78 - x) * 0.0175 * 1 = 368.50
Simplifying the equation, we get:
0.025x + 0.0175(23,456.78 - x) = 368.50
Now we can solve for x:
0.025x + 410.4565 - 0.0175x = 368.50
Combining like terms, we have:
0.0075x + 410.4565 = 368.50
Subtracting 410.4565 from both sides, we get:
0.0075x = 368.50 - 410.4565
Simplifying further, we have:
0.0075x = -41.9565
Dividing both sides by 0.0075, we get:
x = -41.9565 / 0.0075
Calculating x, we find:
x ≈ 5594.20
So, approximately $5594.20 is invested in the 2½ percent fund.
To find the amount invested in the 1¾ percent fund, we subtract x from the total investment amount:
Amount in 1¾ percent fund = 23,456.78 - 5594.20 ≈ $17,862.58
Therefore, approximately $17,862.58 is invested in the 1¾ percent fund.