Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.)
P = $1100, r = 7% compounded semiannually, t = 14 years


To calculate the compound amount, we use the compound interest formula:

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

Where:
- $ A $ is the compound amount (the total after interest).
- $ P = 1100 $ is the principal (initial amount).
- $ r = 7\% = 0.07 $ is the annual interest rate (as a decimal).
- $ n = 2 $ since the interest is compounded semiannually.
- $ t = 14 $ years.

### Step-by-step calculation:

1. **Calculate the periodic interest rate**:
   \[
   \frac{r}{n} = \frac{0.07}{2} = 0.035
   \]

2. **Calculate the number of periods**:
   \[
   nt = 2 \times 14 = 28
   \]

3. **Apply these values to the compound interest formula**:
   \[
   A = 1100 \left(1 + 0.035\right)^{28}
   \]
   \[
   A = 1100 \left(1.035\right)^{28}
   \]
   \[
   A \approx 1100 \times 2.6898
   \]

4. **Final Calculation**:
   \[
   A \approx 2958.78
   \]

Thus, the compound amount after 14 years is approximately **$2958.78**.

Do you want details on any step or have any questions?

### Related Questions:
1. How does the compounding frequency affect the total amount?
2. What would happen if the interest rate were 5% instead of 7%?
3. How does simple interest compare to compound interest in this scenario?
4. What if the interest were compounded quarterly instead of semiannually?
5. What is the formula for continuous compounding, and how would it apply here?

**Tip:** The more frequently interest is compounded, the higher the final amount will be due to interest being calculated more often.

Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.) P = $1100, r = 7% compounded semiannually, t = 14 years

Learn how to calculate the compound interest for a principal of $1100 with an interest rate of 7%, compounded semiannually over 14 years. This example uses the compound interest formula to arrive at the final amount of approximately $2958.78.

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