A university alumni association invested part of \( \$ 22,000 \) in preferred stock that earns \( 8 \% \) annual simple interest, and the remainder in a municipal bond that earns \( 7 \% \) annual simple interest. The amount of interest earned each year is \( \$ 1,610 \). How much was invested in each account? at \( 7 \% \quad \$ \square \) at \( 8 \% \)\( \$ \square \)

Let's define the amount invested in municipal bonds at \( 7\% \) as \( x \) dollars. Therefore, the amount invested in preferred stock at \( 8\% \) will be \( 22,000 - x \) dollars. The interest earned from the municipal bonds can be expressed as \( 0.07x \) and from the preferred stock as \( 0.08(22,000 - x) \). We can set up the equation based on the total interest earned: \[ 0.07x + 0.08(22,000 - x) = 1,610 \] Expanding the equation: \[ 0.07x + 1,760 - 0.08x = 1,610 \] Combining like terms: \[ -0.01x + 1,760 = 1,610 \] Solving for \( x \): \[ -0.01x = 1,610 - 1,760 \] \[ -0.01x = -150 \] \[ x = 15,000 \] So, the amount invested in municipal bonds at \( 7\% \) is \( \$ 15,000 \). The amount invested in preferred stock is: \[ 22,000 - x = 22,000 - 15,000 = 7,000 \] Thus, the amounts invested are: at \( 7 \% \quad \$ 15,000 \) at \( 8 \% \quad \$ 7,000 \)