9. You borrowed \( \$ 95 \) for 1 year at \( 5.2 \% \) interest that is compounded semi annually. What will you pay back in full? Use dollar sign, commas, and decimals in your answers!!!! for Example \( \$ 49,555.13 \)

To calculate the amount you need to pay back with compound interest, you can use the **Compound Interest Formula**: \[ \text{Future Value} (FV) = P \times \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( P \) = Principal amount (\$95) - \( r \) = Annual interest rate (5.2% or 0.052) - \( n \) = Number of times interest is compounded per year (2 for semi-annually) - \( t \) = Time in years (1 year) **Step-by-Step Calculation:** 1. **Plug in the values:** \[ FV = 95 \times \left(1 + \frac{0.052}{2}\right)^{2 \times 1} \] 2. **Simplify inside the parentheses:** \[ FV = 95 \times \left(1 + 0.026\right)^2 \] \[ FV = 95 \times (1.026)^2 \] 3. **Calculate \( (1.026)^2 \):** \[ 1.026 \times 1.026 = 1.052676 \] 4. **Multiply by the principal:** \[ FV = 95 \times 1.052676 = 100.00422 \] 5. **Round to the nearest cent:** \[ FV \approx \$100.00 \] **Final Answer:** \[ \$100.00 \]