Question

A total of $46,000 is invested in two corporate bonds that pay 6.75% and 7.25% simple interest. The investor wants an annual interest income of $3245 from the investments. What is the most that can be invested in the 6.75% bond?

Answer 1

The most to be invested in Bond X (pays 6.75%) is $18,000

Step-by-step explanation:

Hi, first, we have to set 2 equations. Let "X" be the bond that returns 6.75% and "Y" the bond that returns 7.25%.

`X+Y=46,000`

We also know that from both investments, the investors want $3,245, therefore:

`0.0675X+0.0725Y=3,245`

Now, we substitute Y for 46,000-X

and this is what we get.

`0.0675X+0.0725(46,000-X)=3,245`

`0.0675X+3,335-0.0725X=3,245`

`-90=-0.005X`

`X=(90)/(0.005) =18,000`

So, the most that can be invested in the 6.75% bond is $18,000

Best of luck.