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A retired woman has $80,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.How much the woman should invest in each option to sustain exactly a $6,000 annual return.bond $ CD$

Answer :

Explanation:

Let x be the amount the woman invests in the 15% bond. Then the amount she invested in her CD is given by:

[tex]80000\text{ - x}[/tex]

Now, the interest she receives from the 15% bond is given by:

[tex]0.15x[/tex]

while the interest she receives from the 7% CD is given by:

[tex]0.07(80000\text{ - x})\text{ = 5600 - 0.07x}[/tex]

Now, given that her total annual interest is $6,000, then

[tex]0.15x+5600-0.07x=6000[/tex]

this is equivalent to:

[tex]0.08x=6000-5600[/tex]

solving for x, we obtain the amount the woman invests in the 15% bond:

[tex]x=5000[/tex]

Therefore, the amount of dollars she will be able to invest in her CD is

[tex]$ 80000- $5000=$ 75000 $[/tex]

Thus, we can conclude that the correct answer is:

Answer:

The amount the woman invests in the 15% bond:

$5000

Amount of dollars she will be able to invest in her CD:

$75000

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