Questions: Use the table to find both the compound amount and the compound interest on 9800 at 2% for 3 years. Interest is compounded semiannually. Click the icon to view the compound interest table. What is the compound amount? (Round to the nearest cent as needed.)

Solution Steps

To solve this problem, we need to use the formula for compound interest. The formula for compound interest when interest is compounded semiannually is:

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

where:

• \( A \) is the compound amount
• \( P \) is the principal amount (\$9800)
• \( r \) is the annual interest rate (2% or 0.02)
• \( n \) is the number of times interest is compounded per year (2 for semiannually)
• \( t \) is the time the money is invested for in years (3 years)

Once we have the compound amount, the compound interest can be found by subtracting the principal from the compound amount.

Using the formula for compound interest:

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

we substitute the values:

• \( P = 9800 \)
• \( r = 0.02 \)
• \( n = 2 \)
• \( t = 3 \)

Calculating:

\[ A = 9800 \left(1 + \frac{0.02}{2}\right)^{2 \cdot 3} = 9800 \left(1 + 0.01\right)^{6} = 9800 \left(1.01\right)^{6} \]

Evaluating \( (1.01)^{6} \):

\[ A \approx 9800 \cdot 1.061520 = 10402.9 \]

The compound interest \( CI \) is given by:

\[ CI = A - P \]

Substituting the values:

\[ CI = 10402.9 - 9800 = 602.9 \]

Final Answer