# Math Help - Investment problem

1. ## Investment problem

I'm having a hard time figuring out where to start on this problem.

"If Ben invests \$4000 at 4% interest per year, how much additional money must be invested at 5½% annual interest to ensure that the interest he receives each year is 4½% of the total amount invested?"

Thanks for the help.

2. Hello,

Your question isn't as detailed as I might like, but it might have been given to you that way, so I'll work with what I have. I'm assuming that we are only worried about the first year (this problem would not have solution if we needed to get 4.5% of the total every year after considering compound interest).

So as to how to start this, you know a few things.

Let A represent the additonal investment, after the first 4000.

$Interest Gained = (4000 * 0.04) + (A * 0.055)$
because you gain 4% interest on the 4000 and 5.5% on the additional investment.

$Desired Interest = 0.045*(4000 + A)$
because we want to earn 4.5% of the total amount invested

So as far as I can tell, to solve your question you need to make the interest gained equal to the desired interest and then solve for A.

That should be a pretty good start. Let me know if you're still having trouble.