How to Calculate Interest Rates for Investments

What is the interest rate of each investment?

The annual interest on a $7000 investment exceeds the interest earned on a $5000 investment by $202. The $7000 is invested at a 0.6% higher rate of interest than the $5000.

Answer:

To find the interest rate of each investment, create equations from the information provided. Let's denote the interest rate of the $5000 investment as 'r' and the $7000 investment as 'r + 0.006%.'

Create equations from the information provided, one indicating the difference in interest earned by the two investments, and the other asserting that both interest rates must be positive. Solve these equations to find the interest rates of the investments.

The interest rate for the $5000 investment is \"x%\" and the interest rate for the $7000 investment is \"x + 0.6%.\"

Explanation:

To find the interest rate of each investment, one can create two equations based on the information provided in the question. Let's denote the interest rate of the $5000 investment as 'r,' and because the $7000 investment has a 0.6% higher rate, we'll use 'r+0.006' for its rate. The first equation we can formulate from the information that the interest from the $7000 investment exceeds that of the $5000 investment by $202, would be $7000(r + 0.006) - $5000r = 202.

Secondly, we know that both quantities are positive, thus their interest rates must also be positive. This gives the second equation as r > 0 and (r+0.006) > 0. By solving these equations, you will be provided with the interest rates for both of your investments.

Remember that simple interest is calculated as principle amount multiplied by interest rate, with examples like the $100 deposit at a simple interest rate of 5% held for three years yielding $100 x 0.05 x 3 = $15.