​$2000 for 3 years at 7​% compounded semiannually.
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Part 1
The amount in the account is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the amount in the account after 3 years at 7% interest compounded semiannually, we use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ 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 or borrowed for, in years.

Given:
- $ P = 2000 $
- $ r = 7\% = 0.07 $
- $ n = 2 $ (since it's compounded semiannually)
- $ t = 3 $ years

Substitute the given values into the formula:

\[
A = 2000 \left(1 + \frac{0.07}{2}\right)^{2 \times 3}
\]

\[
A = 2000 \left(1 + 0.035\right)^6
\]

\[
A = 2000 \left(1.035\right)^6
\]

Now, calculate $ \left(1.035\right)^6 $ and then multiply by 2000.

\[
A \approx 2000 \times 1.233004
\]

\[
A \approx 2466.01
\]

So, the amount in the account after 3 years is approximately **$2466.01**.

Would you like a more detailed explanation or have any questions? Here are some related questions:

1. What would be the amount if the interest was compounded annually instead?
2. How would the amount change if the interest rate was 5% instead of 7%?
3. What if the interest was compounded quarterly? How would that affect the final amount?
4. How much interest is earned over the 3 years?
5. How does the compound interest formula differ from the simple interest formula?

**Tip:** Compounding more frequently (e.g., semiannually vs. annually) results in a slightly higher amount due to interest being calculated on the previously earned interest more often.

$2000 for 3 years at 7% compounded semiannually. The amount in the account is ​$ (Do not round until the final answer. Then round to the nearest cent as needed.)

Calculate the amount in the account after 3 years with $2000 at 7% interest compounded semiannually. This problem covers the compound interest formula, exponential growth concepts, and step-by-step calculations, making it suitable for students in Grades 10-12.

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