Questions: Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps. Principal Rate Compounded Time 1,465 0.6% Semiannually 13 years The future value is , and the compound interest is .

Solution Steps

To solve this problem, we need to use the compound interest formula to find the future value and then calculate the compound interest. The compound interest formula is:

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

where:

• \( A \) is the future value
• \( P \) is the principal amount ($1,465)
• \( r \) is the annual interest rate (0.6% or 0.006)
• \( n \) is the number of times interest is compounded per year (semiannually, so \( n = 2 \))
• \( t \) is the time the money is invested for in years (13 years)

The compound interest is then calculated as the future value minus the principal.

Using the compound interest formula:

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

we substitute the values:

• \( P = 1465 \)
• \( r = 0.006 \)
• \( n = 2 \)
• \( t = 13 \)

Calculating gives:

\[ A = 1465 \left(1 + \frac{0.006}{2}\right)^{2 \times 13} = 1465 \left(1 + 0.003\right)^{26} = 1465 \left(1.003\right)^{26} \approx 1583.66 \]

The compound interest is calculated as:

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

Substituting the values:

\[ \text{Compound Interest} = 1583.66 - 1465 = 118.66 \]

Final Answer