Why is the required investment negative in this interest rate problem?

[Omid]

A man invest $1800 at 9/2 % and $2000 at 5%. How much must he invest at 6% so that the average income on the three investments will be 5% ?
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I set an equation and solved, then found he must invest -$1322 at 6%
What does the negative sign mean ? Probably I have made a mistake. If so please let me know.
Thanks

 

[faust9]

What equation did you use? Did you use continuous interest or regular interest?

 

[Tide]

I think you made an arithmetic error or set up the equations incorrectly. I came up with a positive number.

 

[Omid]

I think you made an arithmetic error or set up the equations incorrectly. I came up with a positive number.

Was the number 1322 or not ?

 

[Tide]

No it was not.

 

[Omid]

My equation is :
[(0.045)(1800) + 0.05(2000) + 0.06(x)] / 3 = 0.5(1800 + 2000 +x)

 

[Omid]

So please help me to finde the right answer.

 

[faust9]

I'm sorry, I misread your question.

 

[Tide]

My equation is :
[(0.045)(1800) + 0.05(2000) + 0.06(x)] / 3 = 0.5(1800 + 2000 +x)

That should be 0.05 and NOT 0.5 on the right hand side.

 

[Omid]

That should be 0.05 and NOT 0.5 on the right hand side.

You mean everything is ok except that 0.5 ?

 

[Tide]

You mean everything is ok except that 0.5 ?

Actually there is another problem - you don't need to divide by 3 on the left hand side! The 0.05 on the right side assures that you have the average interest rate correct!

 

[Omid]

Ok, thanks a lot.

 

[Tide]

Most welcome!