Questions: Find the compound amount for the deposit and the amount of interest earned. 440 at 6.6% compounded semiannually for 15 years The compound amount after 15 years is (Do not round until the final answer. Then round to the nearest cent as needed.) The amount of interest earned is (Do not round until the final answer. Then round to the nearest cent as needed.)

Solution Steps

To find the compound amount for the deposit, we use 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 (initial deposit).
• \( r \) 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.

After calculating the compound amount, the interest earned can be found by subtracting the principal from the compound amount.

To find the compound amount \( A \) after 15 years for a principal amount \( P = 440 \) dollars at an annual interest rate \( r = 0.066 \) compounded semiannually (\( n = 2 \)), we use the formula:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the values:

\[ A = 440 \left(1 + \frac{0.066}{2}\right)^{2 \times 15} \]

Calculating this gives:

\[ A \approx 1165.3659432307231 \]

Rounding to the nearest cent, we find:

\[ A \approx 1165.37 \]

The interest earned can be calculated by subtracting the principal from the compound amount:

\[ \text{Interest Earned} = A - P \]

Substituting the values:

\[ \text{Interest Earned} = 1165.3659432307231 - 440 \]

Calculating this gives:

\[ \text{Interest Earned} \approx 725.3659432307231 \]

Rounding to the nearest cent, we find:

\[ \text{Interest Earned} \approx 725.37 \]

Final Answer