Question Help: Video Submit Question Question 3 \( 0 / 3 \) pts 3 96 Details Find the final amount of money in an account if \( \$ 4,100 \) is deposited at \( 5 \% \) interest compounded annually and the money is left for 7 years. The final amount is \( \$ \) \( \square \) . Round answer to 2 decimal places Submit Question Question 4 \( 0 / 5 \) pts 3 98 Details

To find the final amount of money in an account after depositing $4,100 at 5% interest compounded annually for 7 years, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{100} \right)^n \] where: - \( A \) is the final amount of money in the account - \( P \) is the principal amount (initial deposit) - \( r \) is the annual interest rate (in %) - \( n \) is the number of years the money is left in the account Given: - \( P = \$4,100 \) - \( r = 5\% \) - \( n = 7 \) years Substitute the values into the formula: \[ A = 4100 \left( 1 + \frac{5}{100} \right)^7 \] Now, we can calculate the final amount of money in the account. Calculate the value by following steps: - step0: Calculate: \(4100\left(1+\frac{5}{100}\right)^{7}\) - step1: Reduce the fraction: \(4100\left(1+\frac{1}{20}\right)^{7}\) - step2: Add the numbers: \(4100\left(\frac{21}{20}\right)^{7}\) - step3: Simplify: \(4100\times \frac{21^{7}}{20^{7}}\) - step4: Rewrite the expression: \(20\times 205\times \frac{21^{7}}{20^{7}}\) - step5: Reduce the numbers: \(205\times \frac{21^{7}}{20^{6}}\) - step6: Rewrite the expression: \(5\times 41\times \frac{21^{7}}{20^{6}}\) - step7: Rewrite the expression: \(5\times 41\times \frac{21^{7}}{5^{6}\times 4^{6}}\) - step8: Reduce the numbers: \(41\times \frac{21^{7}}{5^{5}\times 4^{6}}\) - step9: Multiply: \(\frac{41\times 21^{7}}{12800000}\) The final amount of money in the account after depositing $4,100 at 5% interest compounded annually for 7 years is approximately $5,769.11.