A total of $22,000 is invested in two municipal bonds that pay 4.25% and 5.75% simple interest. The investor wants an annual interest income of $1085 from the investments. What amount should be invested in the 4.25% bond?
If $x is at 4.25%, the rest (22000-x) is at 5.75%
So, just add up the interest received:
.0425x + .0575(22000-x) = 1085
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume x represents the amount invested in the 4.25% bond.
The amount invested in the 5.75% bond would then be (22000 - x), as the total invested is $22,000.
Now, we can set up the equation for the interest earned from each bond:
Interest from the 4.25% bond = (x * 0.0425)
Interest from the 5.75% bond = ((22000 - x) * 0.0575)
According to the problem, the total annual interest income should be $1085, so we can set up the following equation:
(x * 0.0425) + ((22000 - x) * 0.0575) = 1085
Now, let's solve this equation to find the value of x.
Multiply the percentages with the respective amounts invested:
0.0425x + 0.0575(22000 - x) = 1085
Multiply the terms inside the parentheses:
0.0425x + 1265 - 0.0575x = 1085
Combine like terms:
-0.015x + 1265 = 1085
Subtract 1265 from both sides:
-0.015x = -180
Divide by -0.015:
x = -180 / -0.015
x = 12,000
Therefore, the amount that should be invested in the 4.25% bond is $12,000.