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* = $2900, *r* = 2%, *t* = 12

1

2

,

 compounded semiannually

To find the accumulated amount $ A $ when the interest is compounded semiannually, we use the compound interest formula:

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

Where:
- $ P = 2900 $ (the principal amount)
- $ r = 0.02 $ (the annual interest rate, 2%)
- $ t = \frac{12}{12} = 1 $ (the time period in years)
- $ n = 2 $ (the number of compounding periods per year, since it's compounded semiannually)

Now, let's calculate the accumulated amount:

\[
A = 2900 \left(1 + \frac{0.02}{2}\right)^{2 \times 1}
\]

\[
A = 2900 \left(1 + 0.01\right)^2
\]

\[
A = 2900 \times 1.01^2
\]

\[
A = 2900 \times 1.0201
\]

\[
A = 2958.29
\]

So, the accumulated amount $ A $ is **$2,958.29**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the accumulated amount change if the interest rate increased to 3%?
2. What would the accumulated amount be after 2 years instead of 1 year?
3. How does the number of compounding periods per year affect the accumulated amount?
4. What is the formula for continuous compounding, and how does it differ from this one?
5. How would the accumulated amount change if it were compounded quarterly instead of semiannually?

**Tip:** When dealing with compound interest, the more frequently the interest is compounded, the higher the accumulated amount will be.

Learn how to calculate the accumulated amount when a principal of $2900 is invested at an annual interest rate of 2% compounded semiannually over 1 year. Follow a step-by-step solution using the compound interest formula. Suitable for high school students and anyone interested in financial mathematics.

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