Expert: Jack Cheng - 12/14/2006

Question
A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The investor wants an annual interest income of $990 from the investments. What amount should be invested in the 7.5% bond?

What are the steps to setting up the systems needed to solve this question?

Answer
Hi Christine,

I am assuming that the investor wants EXACTLY $990 of income. Otherwise, just make the investment for the 7.5% bond zero; you get more money that way :)

[FOR BEST RESULT, VIEW WITH A FIXED-SIZE FONT LIKE COURIER.]

We can set up equations to solve this:

x = amount invested in 7.5% bond
y = amount invested in 9% bond

x + y = 12,000        sum of both bonds is 12,000
   y = 12,000 - x

0.075x + 0.09y = 990       total interest should be 990
0.075x + 0.09(12,000-x) = 990
0.075x + 0.09(12,000) - 0.09x = 990
-0.15x = -90
    x = 90/0.15 = 600

So he should invest $600 dollars in the 7.5% bond to get exactly $990 of interest income. Whatever else should go to the 9% bond.

I hope this helps,
Jack