Question Allison accumulated \( \$ 7,000 \) in credit card debt. If the interest rate is \( 15 \% \) per year and she does not make any paym 3 years, how much will she owe on this debt in 3 years for quarterly compounding? Round your answer to the nearest cent. Do NOT round until you calculate the final answer

To calculate the amount Allison will owe on her credit card debt in 3 years with quarterly 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 (initial amount of money). - \( r \) is the annual interest rate (in decimal form). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for in years. Given: - \( P = \$7,000 \) - \( r = 15\% = 0.15 \) - \( n = 4 \) (quarterly compounding) - \( t = 3 \) years Substitute the given values into the formula: \[ A = 7000 \left( 1 + \frac{0.15}{4} \right)^{4 \times 3} \] Now, we can calculate the amount Allison will owe on her credit card debt in 3 years with quarterly compounding. Calculate the value by following steps: - step0: Calculate: \(7000\left(1+\frac{0.15}{4}\right)^{4\times 3}\) - step1: Divide the terms: \(7000\left(1+\frac{3}{80}\right)^{4\times 3}\) - step2: Add the numbers: \(7000\left(\frac{83}{80}\right)^{4\times 3}\) - step3: Multiply the numbers: \(7000\left(\frac{83}{80}\right)^{12}\) - step4: Simplify: \(7000\times \frac{83^{12}}{80^{12}}\) - step5: Rewrite the expression: \(40\times 175\times \frac{83^{12}}{80^{12}}\) - step6: Rewrite the expression: \(40\times 175\times \frac{83^{12}}{40^{12}\times 2^{12}}\) - step7: Reduce the numbers: \(175\times \frac{83^{12}}{40^{11}\times 2^{12}}\) - step8: Rewrite the expression: \(25\times 7\times \frac{83^{12}}{40^{11}\times 2^{12}}\) - step9: Rewrite the expression: \(25\times 7\times \frac{83^{12}}{5^{11}\times 8^{11}\times 2^{12}}\) - step10: Rewrite the expression: \(5^{2}\times 7\times \frac{83^{12}}{5^{11}\times 8^{11}\times 2^{12}}\) - step11: Reduce the numbers: \(7\times \frac{83^{12}}{5^{9}\times 8^{11}\times 2^{12}}\) - step12: Multiply the fractions: \(\frac{7\times 83^{12}}{5^{9}\times 8^{15}}\) After calculating, Allison will owe approximately $10,888.18 on her credit card debt in 3 years with quarterly compounding.