Question An account is opened with an initial deposit of \( \$ 700 \) and earns \( 3.3 \% \) interest compounded semi-annually. What will the account be worth in 3 years? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

To determine the future value of an account with compound interest, we'll use the **compound interest formula**: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) = the amount of money accumulated after \( t \) years, including interest. - \( P \) = the principal amount (initial deposit) = \$700. - \( r \) = annual interest rate (in decimal) = 3.3% = 0.033. - \( n \) = number of times the interest is compounded per year = 2 (semi-annually). - \( t \) = number of years the money is invested = 3. **Step 1: Plug the values into the formula** \[ A = 700 \left(1 + \frac{0.033}{2}\right)^{2 \times 3} \] \[ A = 700 \left(1 + 0.0165\right)^6 \] \[ A = 700 \left(1.0165\right)^6 \] **Step 2: Calculate \( \left(1.0165\right)^6 \)** To compute \( 1.0165^6 \) without rounding until the final step: \[ 1.0165^6 \approx 1.1031798 \] **Step 3: Multiply by the principal** \[ A = 700 \times 1.1031798 \approx 772.22586 \] **Step 4: Round to the nearest cent** \[ A \approx \$772.23 \] **Final Answer:** After 3 years, the account will be worth **\$772.23**.