You would like to invest in $12,000 in two different bonds. Some of the amount will be invested in treasury bonds at 10% annual interest and the rest in municipal bonds at 15%. What amount should be invested in each type of bond rate if the annual yield expected is $1,440?
x = amt invested at 0.10
y = amt invested at 0.15
0.10x + 0.15y = 1440
x + y = 12000
Solve for x and y simultaneously
If you are correct,
x = $7,200
y = $4,800
To determine the amount that should be invested in each type of bond, we can set up a system of equations based on the given information.
Let's assume that x represents the amount invested in treasury bonds, and y represents the amount invested in municipal bonds.
From the given information, we know two things:
1) The total amount invested should be $12,000: x + y = 12,000.
2) The total yield expected (annual interest) is $1,440. This can be calculated by adding the interest earned from the treasury bonds (10% * x) to the interest earned from the municipal bonds (15% * y): 0.10x + 0.15y = 1,440.
Now we have a system of two equations with two variables:
Equation 1: x + y = 12,000
Equation 2: 0.10x + 0.15y = 1,440
We can solve this system of equations to find the values of x and y.
One way to solve this system is by using substitution:
1) Rearrange Equation 1 to solve for x: x = 12,000 - y.
2) Substitute x in Equation 2 with the value from step 1: 0.10(12,000 - y) + 0.15y = 1,440.
3) Simplify and solve for y: 1,200 - 0.10y + 0.15y = 1,440.
Combine like terms: 0.05y = 240.
Divide both sides by 0.05: y = 4,800.
4) Substitute y in Equation 1 to find x: x + 4,800 = 12,000.
Solve for x: x = 7,200.
Therefore, you should invest $7,200 in treasury bonds (10% annual interest) and $4,800 in municipal bonds (15% annual interest) to achieve the expected annual yield of $1,440.