Models and Applications- Investments

Question

A retired woman has $50,000 to invest but needs to make $3,000 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 the CD?

Answer 1

This is a funny problem because, it seems to be asking ONLY that the interest from the 15% bond equals $3000. In fact, whatever she doesn't invest in the 15% bond will also be making interest but at 7%. But anyway . . .

Since "x" is the amount the woman invests in the 15% bond, then the interest she earns with the bond (in a year) is 0.15x. Since she wants $3000 in interest, then 0.15x = 3000 so x = 3000/0.15 = $20,000.

That leaves $30,000 to invest in the CD.

Answer 2

0.15x + 0.07(50000 - x) = 3000

Can you solve for x and answer?