Calculate Interest Rates of Investments

What is the annual interest on a $5000 investment compared to a $3000 investment?

The annual interest on a $5000 investment exceeds the interest earned on a $3000 investment by $185. What is the interest rate of each investment?

Answer:

The interest rate on the $5000 investment is 8.5% and the interest rate on the $3000 investment is 8%.

Let's denote the interest rate on the $5000 investment as x (in decimal form) and the interest rate on the $3000 investment as y (in decimal form). According to the given information, the annual interest on the $5000 investment exceeds the interest earned on the $3000 investment by $185, which can be expressed as:

$5000x - $3000y = $185

It is also stated that the $5000 is invested at a 0.5% higher rate of interest than the $3000, which can be expressed as:

x = y + 0.005

By solving these two equations simultaneously, we find that the interest rate on the $5000 investment is 8.5% and the interest rate on the $3000 investment is 8%.