A total of 8000 dollars is invested in two funds paying 4 percent and 5 percent annual interest,. The combined interest for the year is 350 dollars. How much of the 8000 dollars is invested in each fund? Put the amount of money that should be invested in the 4 percent account in part I and the amount in 5 percent in part II.
What amount should be invested in the 4 percent account?
What amount should be invested in the 5 percent account?
You have two equations in two unknowns to solve.
x + y = 8000
.04x + .05y = 350
solve for x and y then continue : )
$Po invested at 4%.
$(8000-Po) invested at 5%
Po*0.04*1 + (8000-Po)*0.05*1 = 350.
0.04Po + 400 - 0.05Po = 350,
Po = $5000.
8000-Po = 8000-5000 = $3000.
To solve this problem, let's assume that the amount invested in the 4 percent account is represented by "x" dollars.
According to the problem, the total amount invested is $8000. Therefore, the amount invested in the 5 percent account can be represented as (8000 - x) dollars.
Now, we know that the interest obtained from the 4 percent account is 4% of "x" dollars, and the interest obtained from the 5 percent account is 5% of (8000 - x) dollars.
The combined interest for the year is $350. So, we can set up the following equation:
0.04x + 0.05(8000 - x) = 350
Simplifying the equation,
0.04x + 400 - 0.05x = 350
Combining like terms,
-0.01x + 400 = 350
Subtracting 400 from both sides,
-0.01x = -50
Dividing by -0.01,
x = 5000
Therefore, $5000 should be invested in the 4 percent account.
To find the amount that should be invested in the 5 percent account, we subtract the amount invested in the 4 percent account from the total amount, which gives:
8000 - 5000 = 3000
Therefore, $3000 should be invested in the 5 percent account.
To solve this problem, we can use a system of equations.
Let's assume the amount invested in the 4 percent account is 'x' dollars.
Then, the amount invested in the 5 percent account would be '8000 - x' dollars (as the total invested amount is $8000).
Now, we can set up the equations:
Equation 1: (4 percent interest)
The interest earned from the 4 percent account would be: x * 0.04
Equation 2: (5 percent interest)
The interest earned from the 5 percent account would be: (8000 - x) * 0.05
We know from the problem statement that the total interest earned is $350. So, we can set up the equation:
Equation 3: (total interest)
x * 0.04 + (8000 - x) * 0.05 = 350
Now, we can solve this system of equations to find the values of 'x' and '8000 - x'.
Step 1: Simplify equation 3:
0.04x + 0.05(8000 - x) = 350
0.04x + 400 - 0.05x = 350
-0.01x = -50
x = (-50) / (-0.01)
x = 5000
Therefore, the amount that should be invested in the 4 percent account (part I) is $5000.
To find the amount to be invested in the 5 percent account (part II), subtract the amount invested in the 4 percent account from the total investment:
8000 - 5000 = 3000
Therefore, the amount that should be invested in the 5 percent account (part II) is $3000.