Find the accumulated amount *A* if the principal *P* is invested at the interest rate of *r*/year for *t* years. (Use a 365-day year. Round your answer to the nearest cent.)

*P* = $2800, *r* = 6%, *t* = 12

1

2

,

 compounded semiannually

*A* = $ 

To find the accumulated amount $ A $, we use the compound interest formula:

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

Where:
- $ A $ = the accumulated amount
- $ P $ = the principal amount ($2800)
- $ r $ = the annual interest rate (6% or 0.06)
- $ n $ = the number of times the interest is compounded per year (semiannually means $ n = 2 $)
- $ t $ = the time the money is invested for in years (12 years)

### Step-by-step calculation:

1. **Substitute the values into the formula**:
   \[
   A = 2800 \left( 1 + \frac{0.06}{2} \right)^{2 \times 12}
   \]

2. **Simplify the terms**:
   \[
   A = 2800 \left( 1 + 0.03 \right)^{24} = 2800 \times (1.03)^{24}
   \]

3. **Calculate $ (1.03)^{24} $**:
   \[
   (1.03)^{24} \approx 1.981
   \]

4. **Multiply by the principal**:
   \[
   A = 2800 \times 1.981 = 5546.80
   \]

So, the accumulated amount $ A $ is **$5546.80**.

Would you like more details on any part of this process? Here are five related questions for practice:

1. What would be the accumulated amount if compounded quarterly?
2. How would the accumulated amount change if the interest rate were 5% instead of 6%?
3. What is the accumulated amount if the time is reduced to 10 years instead of 12?
4. How would continuous compounding affect the final amount?
5. What is the total interest earned on the investment?

**Tip**: When interest is compounded more frequently, the accumulated amount increases, even if the rate and time remain the same.

Find the accumulated amount A if the principal P is invested at the interest rate of r per year for t years. P = $2800, r = 6%, t = 12, compounded semiannually.

Learn how to calculate the accumulated amount for a principal of $2800 invested at 6% interest compounded semiannually over 12 years. Using the compound interest formula, this detailed step-by-step guide walks you through key concepts of financial mathematics, including exponential growth.

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