Question If \( \$ 200 \) is borrowed with an interest of \( 18.0 \% \) compounded monthly, what is the total amount of money needed to pay back in 1 year? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

To find the total amount of money needed to pay back in 1 year when borrowing $200 with an interest of 18.0% compounded monthly, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] where: - \( A \) is the total amount of money needed to pay back, - \( P \) is the principal amount borrowed ($200), - \( r \) is the annual interest rate (18.0% or 0.18), - \( n \) is the number of times the interest is compounded per year (12 for monthly compounding), - \( t \) is the time in years (1 year). Substitute the given values into the formula: \[ A = 200 \left( 1 + \frac{0.18}{12} \right)^{12 \cdot 1} \] Now, we can calculate the total amount of money needed to pay back in 1 year. Calculate the value by following steps: - step0: Calculate: \(200\left(1+\frac{0.18}{12}\right)^{12}\) - step1: Divide the terms: \(200\left(1+\frac{3}{200}\right)^{12}\) - step2: Add the numbers: \(200\left(\frac{203}{200}\right)^{12}\) - step3: Simplify: \(200\times \frac{203^{12}}{200^{12}}\) - step4: Reduce the numbers: \(1\times \frac{203^{12}}{200^{11}}\) - step5: Multiply: \(\frac{203^{12}}{200^{11}}\) The total amount of money needed to pay back in 1 year when borrowing $200 with an interest of 18.0% compounded monthly is approximately $239.12. Therefore, the total amount of money needed to pay back in 1 year is $239.12.