I have money to invest at 7.5% interest. If I had $3,000 more to invest, I could invest at 11%. 11% yields twice as much annual income, how much do I have?

Question

I need help with the equation, please.

Answer 1

To start, the investment of $3,000 at 11% is equal to $3330 after a year. --> $3000*(1+i)=$3,000+AI -->$3,000*(1.11)=$3,330 --> AI = $330.

 

We know now that the $3000 @ 11% investment earns us $330 over a year. We also know that this $330 is twice as much as the investment @ 7.5% --> $330/2 = $165. Our goal from here is to find out what yields an annual income of $165 over a year @ 7.5%. To calculate this we divide $165 by .075. --> X = $165 / 7.5%--> X = 2200

 

To check our work we can say we are to invest $2200 @ 7.5% --> $2200*(1+.075) = $2200+AI --> $2365=$2200+AI -->AI=$165 --> this checks out.

 

Let me know if you have further questions.