Gabe deposits \( \$ 7,000 \) in a certificate of deposit. The annual interest rate is \( 4 \% \), and the interest will be compounded quarterly. How much will the certificate be worth in 5 years? Round your answer to the nearest cent. Do NOT round until you calculate the final answer

To determine the future value of Gabe's certificate of deposit (CD) after 5 years with quarterly compounding 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 investment amount (\$7,000). - \( r \) = the annual interest rate (decimal) (4% or 0.04). - \( n \) = the number of times that interest is compounded per year (4 for quarterly). - \( t \) = the time the money is invested for in years (5 years). **Step-by-Step Calculation:** 1. **Identify the Variables:** \[ P = \$7,000 \\ r = 4\% = 0.04 \\ n = 4 \\ t = 5 \text{ years} \] 2. **Plug the Values into the Formula:** \[ A = 7000 \left(1 + \frac{0.04}{4}\right)^{4 \times 5} \] \[ A = 7000 \left(1 + 0.01\right)^{20} \] \[ A = 7000 \left(1.01\right)^{20} \] 3. **Calculate \( \left(1.01\right)^{20} \):** \[ \left(1.01\right)^{20} \approx 1.220189956040252 \] 4. **Multiply by the Principal:** \[ A = 7000 \times 1.220189956040252 \approx 8541.329692281766 \] 5. **Round to the Nearest Cent:** \[ A \approx \$8,541.33 \] **Final Answer:** After 5 years, the certificate will be worth **\$8,541.33**.