Find the final amount of money in an account if \( \$ 1,200 \) is deposited at \( 2.5 \% \) interest compounded semi-annually and the money is left for 9 years. The final amount is \( \$ \square \) Round to the nearest cent. Question Help: \( \square \) Message instructor Calculator Submit Question

To find the final amount, you can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \(A\) is the amount of money accumulated after n years, including interest, - \(P\) is the principal amount (the initial amount of money), - \(r\) is the annual interest rate (decimal), - \(n\) is the number of times that interest is compounded per year, - \(t\) is the number of years the money is invested or borrowed. Plugging in the values: - \(P = 1200\) - \(r = 0.025\) (which is \(2.5\%\)), - \(n = 2\) (because the interest is compounded semi-annually), - \(t = 9\). Now, substituting those values into the formula: \[ A = 1200 \left(1 + \frac{0.025}{2}\right)^{2 \cdot 9} \] \[ A = 1200 \left(1 + 0.0125\right)^{18} \] \[ A = 1200 \left(1.0125\right)^{18} \] Calculating \( (1.0125)^{18} \) gives approximately \(1.2434\). Now, calculate \(A\): \[ A \approx 1200 \times 1.2434 \approx 1492.08 \] Thus, the final amount in the account after 9 years is approximately \( \$1492.08 \). So, rounding to the nearest cent, the final amount is \( \$ \mathbf{1492.08} \).