In how many years will \( \neq 11.500 \) yield A 375 simple interest at \( 5 \% \) ? \( \begin{array}{lllll}\text { A. } 4 & \text { B. } 5 & \text { C. } 6 & \text { D. } 6 y & \text { E. } 7\end{array} \)

To find the number of years it will take for an amount of \( \neq 11.500 \) to yield a simple interest of \( 375 \) at a rate of \( 5\% \), we can use the formula for simple interest: \[ \text{Simple Interest} = \frac{P \times R \times T}{100} \] Where: - \( P \) is the principal amount (initial amount), - \( R \) is the rate of interest (in %), - \( T \) is the time period (in years). Given: - Principal amount (\( P \)) = \( 11.500 \), - Simple interest (\( SI \)) = \( 375 \), - Rate of interest (\( R \)) = \( 5\% \). We need to find the time period (\( T \)). Substitute the given values into the formula: \[ 375 = \frac{11.500 \times 5 \times T}{100} \] Now, we can solve for \( T \) to find the number of years it will take for the simple interest to be \( 375 \) at a rate of \( 5\% \). Solve the equation by following steps: - step0: Solve for \(T\): \(375=\frac{11.5\times 5T}{100}\) - step1: Simplify: \(375=\frac{23T}{40}\) - step2: Swap the sides: \(\frac{23T}{40}=375\) - step3: Cross multiply: \(23T=40\times 375\) - step4: Simplify the equation: \(23T=15000\) - step5: Divide both sides: \(\frac{23T}{23}=\frac{15000}{23}\) - step6: Divide the numbers: \(T=\frac{15000}{23}\) The number of years it will take for an amount of \( 11.500 \) to yield a simple interest of \( 375 \) at a rate of \( 5\% \) is \( \frac{15000}{23} \) years. To find the approximate value, we can calculate \( \frac{15000}{23} \) to determine the number of years. Calculate the value by following steps: - step0: Calculate: \(\frac{15000}{23}\) The number of years it will take for an amount of \( 11.500 \) to yield a simple interest of \( 375 \) at a rate of \( 5\% \) is approximately \( 652.173913 \) years. Therefore, the correct answer is \( \boxed{7} \) years.