If an amount of $5,000 is invested at a simple interest rate of 3.5% interest per year, how much additional money must be invested at a simple interest rate of 5% per year to ensure that the interest each year is 4% of the total amount invested?

To solve this problem, let's break it down into steps:

Step 1: Calculate the interest earned from the initial investment.
The interest earned from the initial investment of $5,000 at 3.5% per year can be calculated using the formula for simple interest:

\text{{Interest}} = \text{{Principal}} \times \text{{Rate}} \times \text{{Time}}

where Principal is the initial investment, Rate is the interest rate, and Time is the number of years.

\text{{Interest}} = \$5,000 \times 0.035 \times 1

\text{{Interest}} = \$175

Step 2: Determine the total amount that needs to be invested.
Since we want the interest earned each year to be 4% of the total amount invested, we can set up the following equation:

0.04 \times \text{{Total Amount}} = \$175

Divide both sides of the equation by 0.04 to solve for the total amount:

\text{{Total Amount}} = \frac{{\$175}}{{0.04}}

\text{{Total Amount}} = \$4375

Step 3: Calculate the additional amount that needs to be invested.
Since we already have an initial investment of $5,000, we need to calculate the additional amount that needs to be invested to reach a total amount of $4,375.

\text{{Additional Amount}} = \text{{Total Amount}} - \text{{Initial Investment}}

\text{{Additional Amount}} = \$4375 - \$5000

\text{{Additional Amount}} = -\$625

Answer: To ensure that the interest each year is 4% of the total amount invested, an additional amount of $625 must be invested at a simple interest rate of 5% per year.