Nazerhy deposits $ 8,000 in a certificate of deposit. The annual interest rate is 6 % , and the interest will be compounded monthly. How much will the certificate be worth in 10 years? Round your answer to the nearest cent. Do NOT round until you calculate the final answer

1. Identify the formula for compound interest: 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).

- \(r\) is the annual interest rate (decimal).

- \(n\) is the number of times that interest is compounded per year.

- \(t\) is the time the money is invested for in years.

2. Substitute the given values into the formula:

- \(P = 8000\),

- \(r = \frac{6}{100} = 0.06\),

- \(n = 12\),

- \(t = 10\).

3. Calculate the compound interest:

A = 8000 \left(1 + \frac{0.06}{12}\right)^{12 \times 10}

4. Compute the value inside the parentheses:

1 + \frac{0.06}{12} = 1 + 0.005 = 1.005

5. Raise the result to the power of \(120\) (since \(12 \times 10 = 120\)):

1.005^{120} \approx 2.040160365

6. Multiply by the principal:

A=8000\times2.040160365\approx14555.17

7. The certificate will be worth $14555.17 after 10 years.