6. Your bank of choice has an interest rate of \( 1.2 \% \) for a savings account. If you deposit \( \$ 13,000 \) into a new savings account, how much money will be in the account in 25 years?

To find out how much money will be in the account in 25 years, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{100} \right)^n \] Where: - \( A \) is the amount of money in the account after \( n \) years, - \( P \) is the principal amount (initial deposit), - \( r \) is the interest rate, - \( n \) is the number of years. Given: - Principal amount (\( P \)) = $13,000 - Interest rate (\( r \)) = 1.2% - Number of years (\( n \)) = 25 years Substitute the given values into the formula: \[ A = 13000 \left( 1 + \frac{1.2}{100} \right)^{25} \] Now, we can calculate the amount of money in the account after 25 years. Calculate the value by following steps: - step0: Calculate: \(13000\left(1+\frac{1.2}{100}\right)^{25}\) - step1: Divide the terms: \(13000\left(1+\frac{3}{250}\right)^{25}\) - step2: Add the numbers: \(13000\left(\frac{253}{250}\right)^{25}\) - step3: Simplify: \(13000\times \frac{253^{25}}{250^{25}}\) - step4: Rewrite the expression: \(250\times 52\times \frac{253^{25}}{250^{25}}\) - step5: Reduce the numbers: \(52\times \frac{253^{25}}{250^{24}}\) - step6: Rewrite the expression: \(4\times 13\times \frac{253^{25}}{250^{24}}\) - step7: Rewrite the expression: \(4\times 13\times \frac{253^{25}}{2^{24}\times 125^{24}}\) - step8: Rewrite the expression: \(2^{2}\times 13\times \frac{253^{25}}{2^{24}\times 125^{24}}\) - step9: Reduce the numbers: \(13\times \frac{253^{25}}{2^{22}\times 125^{24}}\) - step10: Multiply the fractions: \(\frac{13\times 253^{25}}{2^{22}\times 125^{24}}\) The amount of money in the account after 25 years will be approximately $17,516.86.