Carletta has 23000 dollars to invest. As her financial consultant, you recommend that she invest in Treasury Bills that yield 7%, Treasury Bonds that yield 8%, and corporate bonds that yield 9%. Carletta wants to have an annual income of 1800 dollars, and the amount invested in corporate bonds must be half that invested in Treasury Bills. Find the amount she should place in each investment.

Question

Carletta has 23000 dollars to invest. As her financial consultant, you recommend that she invest in Treasury Bills that yield 7%, Treasury Bonds that yield 8%, and corporate bonds that yield 9%. Carletta wants to have an annual income of 1800 dollars, and the amount invested in corporate bonds must be half that invested in Treasury Bills. Find the amount she should place in each investment.

Answer 1

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!

Answer 2

To find the amount Carletta should invest in each investment, let's denote:

- 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.