Question

A retired woman has $60,000 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%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in her CD?

Answer 1

Let x be the amount the woman invests in the 15% bond, then the amount she invested in her CD is given by $60,000 - x.

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(60,000 - x) = 4,200 - 0.07x

Giving that her total annual interest is $6,000, then

$0.15x+4,200-0.07x=6,000 \\ \\ \Rightarrow0.08x=6,000-4,800=1,200 \\ \\ \Rightarrow x= \frac{1,200}{0.08} = 15,000$

Therefore, the amount of dollars she will be able to invest in her CD is $60,000 - $15,000 = $45,000