Questions: Equal amounts are invested at 3%, 7%, and 8% annual interest. If the three investments yield a total of 684 annual interest, find the total investment.

Solution Steps

To solve this problem, we need to determine the total amount of money invested across three different interest rates. Since equal amounts are invested at each rate, we can set up an equation where the sum of the interest from each investment equals the total annual interest of $684. Let \( x \) be the amount invested at each rate. The equation will be: \( 0.03x + 0.07x + 0.08x = 684 \). Solving this equation will give us the value of \( x \), and the total investment will be \( 3x \).

Let \( x \) be the amount invested at each interest rate. The total interest from the investments can be expressed as: \[ 0.03x + 0.07x + 0.08x = 684 \]

Combine the terms on the left side: \[ (0.03 + 0.07 + 0.08)x = 684 \] This simplifies to: \[ 0.18x = 684 \]

To find \( x \), divide both sides by \( 0.18 \): \[ x = \frac{684}{0.18} = 3800 \]

The total investment across the three accounts is: \[ \text{Total Investment} = 3x = 3 \times 3800 = 11400 \]

Final Answer