If the 7,8,9% amounts are x,y,z, respectively, then we have
x+y+z = 23000
.07x + .08y + .08z = 1800
z = x/2
Just solve that for your answers.
Trés simples!
x+y+z = 23000
.07x + .08y + .08z = 1800
z = x/2
Just solve that for your answers.
Trés simples!
- x: amount invested in Treasury Bills
- y: amount invested in Treasury Bonds
- z: amount invested in corporate bonds
Based on the given information, we can start by setting up the following system of equations:
Equation 1: Carletta wants an annual income of $1800, so the total income from the investments should be equal to $1800:
0.07x + 0.08y + 0.09z = 1800
Equation 2: The total amount invested must be $23,000:
x + y + z = 23000
Equation 3: The amount invested in corporate bonds must be half that invested in Treasury Bills:
z = 0.5x
Now we can solve this system of equations. Let's substitute Equation 3 into Equation 1:
0.07x + 0.08y + 0.09(0.5x) = 1800
Simplifying this equation, we get:
0.07x + 0.08y + 0.045x = 1800
Combining like terms, we have:
0.115x + 0.08y = 1800 (Equation 4)
We can now solve Equations 2 and 4 simultaneously. We will use the substitution method to find the values of x and y.
Substituting z from Equation 3 into Equation 2:
x + y + 0.5x = 23000
1.5x + y = 23000
Rearranging this equation, we get:
y = 23000 - 1.5x (Equation 5)
Now substitute Equation 5 into Equation 4:
0.115x + 0.08(23000 - 1.5x) = 1800
Simplifying and solving for x:
0.115x + 1840 - 0.12x = 1800
-0.005x + 1840 = 1800
-0.005x = -40
x = -40 / -0.005
x = 8000
Now substitute this value of x back into Equation 5 to find y:
y = 23000 - 1.5(8000)
y = 23000 - 12000
y = 11000
Finally, substitute the values of x and y into Equation 3 to find z:
z = 0.5(8000)
z = 4000
Therefore, Carletta should invest $8000 in Treasury Bills, $11000 in Treasury Bonds, and $4000 in corporate bonds.
It is important to note that investing decisions should be made considering various factors, including individual risk tolerance and investment goals. Consultation with a financial advisor is recommended.