Question Edgar accumulated \( \$ 5,000 \) in credit card debt. If the interest rate is \( 20 \% \) per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years with monthly compounding? Round your answer to the nearest cent. Do NOT round until you calculate the final answer Provide your answer below:

To calculate the amount Edgar will owe on his credit card debt after 2 years with monthly compounding, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested or borrowed. Given: - \( P = 5000 \) - \( r = 0.20 \) (20% as a decimal) - \( n = 12 \) (monthly compounding) - \( t = 2 \) Now, we can substitute these values into the formula: \[ A = 5000 \left(1 + \frac{0.20}{12}\right)^{12 \times 2} \] Let's calculate this step by step. 1. Calculate \( \frac{r}{n} \): \[ \frac{0.20}{12} = 0.01666667 \] 2. Calculate \( nt \): \[ 12 \times 2 = 24 \] 3. Calculate \( A \): \[ A = 5000 \left(1 + 0.01666667\right)^{24} \] Now, let's perform the calculations. Calculate the value by following steps: - step0: Calculate: \(5000\left(1+\frac{0.2}{12}\right)^{12\times 2}\) - step1: Divide the terms: \(5000\left(1+\frac{1}{60}\right)^{12\times 2}\) - step2: Add the numbers: \(5000\left(\frac{61}{60}\right)^{12\times 2}\) - step3: Multiply the numbers: \(5000\left(\frac{61}{60}\right)^{24}\) - step4: Simplify: \(5000\times \frac{61^{24}}{60^{24}}\) - step5: Rewrite the expression: \(20\times 250\times \frac{61^{24}}{60^{24}}\) - step6: Rewrite the expression: \(20\times 250\times \frac{61^{24}}{20^{24}\times 3^{24}}\) - step7: Reduce the numbers: \(250\times \frac{61^{24}}{20^{23}\times 3^{24}}\) - step8: Rewrite the expression: \(10\times 25\times \frac{61^{24}}{20^{23}\times 3^{24}}\) - step9: Rewrite the expression: \(10\times 25\times \frac{61^{24}}{10^{23}\times 2^{23}\times 3^{24}}\) - step10: Reduce the numbers: \(25\times \frac{61^{24}}{10^{22}\times 2^{23}\times 3^{24}}\) - step11: Rewrite the expression: \(25\times \frac{61^{24}}{5^{22}\times 2^{22}\times 2^{23}\times 3^{24}}\) - step12: Rewrite the expression: \(5^{2}\times \frac{61^{24}}{5^{22}\times 2^{22}\times 2^{23}\times 3^{24}}\) - step13: Reduce the numbers: \(1\times \frac{61^{24}}{5^{20}\times 2^{22}\times 2^{23}\times 3^{24}}\) - step14: Multiply the fractions: \(\frac{61^{24}}{5^{20}\times 2^{45}\times 3^{24}}\) After performing the calculations, we find that the amount Edgar will owe after 2 years is approximately: \[ A \approx 7434.57 \] Thus, rounding to the nearest cent, Edgar will owe **\$7,434.57** on his credit card debt after 2 years with monthly compounding.