9 Formula 1 point A bank account pays an annual interest rate of \( 21 \% \) with annual compounding. If you deposit \( \$ 8,000 \) today, how much will you have in the account 13 year from today? Round your answer to the nearest penny. Type your answer_

To calculate the future value of the deposit in the bank account after 13 years with an annual interest rate of 21% compounded annually, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] Where: - \( A \) is the future value of the deposit - \( P \) is the principal amount (initial deposit) - \( r \) is the annual interest rate (21% in this case) - \( n \) is the number of times the interest is compounded per year (1 for annual compounding) - \( t \) is the time in years Given: - \( P = \$8,000 \) - \( r = 21\% = 0.21 \) - \( n = 1 \) (annual compounding) - \( t = 13 \) years Substitute the values into the formula: \[ A = 8000 \left( 1 + \frac{0.21}{1} \right)^{1 \times 13} \] Now, we can calculate the future value of the deposit after 13 years. Calculate the value by following steps: - step0: Calculate: \(8000\left(1+0.21\right)^{13}\) - step1: Add the numbers: \(8000\times 1.21^{13}\) - step2: Convert the expressions: \(8000\left(\frac{121}{100}\right)^{13}\) - step3: Simplify: \(8000\times \frac{121^{13}}{100^{13}}\) - step4: Rewrite the expression: \(1000\times 8\times \frac{121^{13}}{100^{13}}\) - step5: Rewrite the expression: \(10^{3}\times 8\times \frac{121^{13}}{10^{26}}\) - step6: Reduce the numbers: \(8\times \frac{121^{13}}{10^{23}}\) - step7: Rewrite the expression: \(8\times \frac{121^{13}}{2^{23}\times 5^{23}}\) - step8: Rewrite the expression: \(2^{3}\times \frac{121^{13}}{2^{23}\times 5^{23}}\) - step9: Reduce the numbers: \(1\times \frac{121^{13}}{2^{20}\times 5^{23}}\) - step10: Multiply the fractions: \(\frac{121^{13}}{2^{20}\times 5^{23}}\) The future value of the deposit after 13 years with an annual interest rate of 21% compounded annually is approximately $95,345.41. Rounding to the nearest penny, the amount in the account 13 years from today will be $95,345.41.