Question

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 1

Step-by-step explanation:

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

`80000\text{ - x}`

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

`0.15x`

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

`0.07(80000\text{ - x})\text{ = 5600 - 0.07x}`

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

`0.15x+5600-0.07x=6000`

this is equivalent to:

`0.08x=6000-5600`

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

`x=5000`

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

`$ 80000- $5000=$ 75000 $`

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