You inherit one million dollars. You invest it all in three accounts for one year. The first account pays \( 4 \% \) compounded annually, the second account pays \( 5 \% \) compounded annually, and the third account pays \( 3 \% \) compounded annually. After one year, you earn \( \$ 44,000 \) in interest. If you invest four times the money into the account that pays \( 4 \% \) compared to \( 3 \% \), how much did you invest in each account? Investment in the \( 4 \% \) account is \( \$ \square \) Investment in the \( 5 \% \) account is \( \$ \square \) Investment in the \( 3 \% \) account is \( \$ \square \)

Let’s denote the amount invested in the \( 3\% \) account as \( x \). According to the problem, the investment in the \( 4\% \) account will be \( 4x \) (four times the investment in the \( 3\% \) account) and the investment in the \( 5\% \) account will be \( y \). The total investments can be set up in the equation: \[ x + 4x + y = 1,000,000 \] This simplifies to: \[ 5x + y = 1,000,000 \quad (1) \] Next, let’s set up the equation for interest earned after one year for each account: \[ 0.03x + 0.04(4x) + 0.05y = 44,000 \] This simplifies to: \[ 0.03x + 0.16x + 0.05y = 44,000 \] which gives us: \[ 0.19x + 0.05y = 44,000 \quad (2) \] Now, we can solve these two equations simultaneously. From equation (1), isolate \( y \): \[ y = 1,000,000 - 5x \quad (3) \] Substitute equation (3) into equation (2): \[ 0.19x + 0.05(1,000,000 - 5x) = 44,000 \] Expanding gives us: \[ 0.19x + 50,000 - 0.25x = 44,000 \] Combine like terms: \[ -0.06x + 50,000 = 44,000 \] Now, isolate \( x \): \[ -0.06x = 44,000 - 50,000 \] \[ -0.06x = -6,000 \] \[ x = \frac{6,000}{0.06} = 100,000 \] Now substitute \( x \) back into equation (3) to find \( y \): \[ y = 1,000,000 - 5(100,000) = 1,000,000 - 500,000 = 500,000 \] Finally, calculate the investment in the \( 4\% \) account: \[ 4x = 4(100,000) = 400,000 \] So, the investments in each account are: Investment in the \( 4\% \) account is \( \$ 400,000 \) Investment in the \( 5\% \) account is \( \$ 500,000 \) Investment in the \( 3\% \) account is \( \$ 100,000 \)