Expert: Steve Holleran - 12/17/2008

Question
Hello:

Here is my question:  An investor has $30,000 to invest at simple interest, one portion at 2% and the other at 5%.
How much must he invest in each account to earn a total return of 4% or $1,200?

I want to try to determine the answers by using the following:
If all of the $30,000 is invested at 2%, this will equal $600. He is now short $600. (Remember the interest must be $1,200.) Any cash removed from the 2% account and invested in the 5% account will earn an extra 3%.  How much does he need to invest at the remaining 3% to earn the shortfall of $600?

Try to determine the answer by using a simple non-algebra calculation if possible. I think division may help determine the answer, but I'm not sure.

I thank you for any helpful reply.

Answer
Hi Kenneth,

It's really not that hard to do it algebraically:

Let x = amount at 5%,  then  (30,000 - x) = amt at 2%

Since I = PR,

1200 = .05x + .02(30,000 - x)

1200 = .05x + 600 - .02x  

600 = .03x   so x = 600 / .02 = 20,000

So, invest $20,000 at 5% and $10,000 at 2% , this gives $1200.

Steve