A principal of \( \$ 3800 \) is invested at \( 7.25 \% \) interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar.

To find the amount of money an investment will be worth after a certain period of time, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{100}\right)^n \] Where: - \( A \) is the amount of money after \( n \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in %), - \( n \) is the number of years. Given: - Principal amount (\( P \)) = $3800 - Annual interest rate (\( r \)) = 7.25% - Number of years (\( n \)) = 12 Substitute the given values into the formula: \[ A = 3800 \left(1 + \frac{7.25}{100}\right)^{12} \] Now, we can calculate the amount of money the investment will be worth after 12 years using the calculator provided. Calculate the value by following steps: - step0: Calculate: \(3800\left(1+\frac{7.25}{100}\right)^{12}\) - step1: Divide the terms: \(3800\left(1+\frac{29}{400}\right)^{12}\) - step2: Add the numbers: \(3800\left(\frac{429}{400}\right)^{12}\) - step3: Simplify: \(3800\times \frac{429^{12}}{400^{12}}\) - step4: Rewrite the expression: \(200\times 19\times \frac{429^{12}}{400^{12}}\) - step5: Rewrite the expression: \(200\times 19\times \frac{429^{12}}{200^{12}\times 2^{12}}\) - step6: Reduce the numbers: \(19\times \frac{429^{12}}{200^{11}\times 2^{12}}\) - step7: Multiply the fractions: \(\frac{19\times 429^{12}}{4096\times 200^{11}}\) The investment of $3800 at an annual interest rate of 7.25% compounded annually will be worth approximately $8801.39 after 12 years.