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* = $2200, *r* = 2%, *t* = 13

1

2

,

 compounded semiannually

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

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

Where:
- $ P $ is the principal amount ($2200),
- $ r $ is the annual interest rate (2%, or 0.02 as a decimal),
- $ t $ is the time in years (13 years),
- $ n $ is the number of times the interest is compounded per year.

Since the interest is compounded semiannually, $ n = 2 $.

Let's plug in the values and calculate $ A $:

\[
A = 2200 \left(1 + \frac{0.02}{2}\right)^{2 \times 13}
\]

\[
A = 2200 \left(1 + 0.01\right)^{26}
\]

\[
A = 2200 \left(1.01\right)^{26}
\]

Now, let's calculate $ (1.01)^{26} $ and then multiply by 2200.

The accumulated amount $ A $ after 13 years with a principal of $2200, compounded semiannually at an annual interest rate of 2%, is approximately **$2849.56**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the accumulated amount change if the interest is compounded quarterly instead of semiannually?
2. What would the accumulated amount be if the interest rate were 3% instead of 2%?
3. How much interest is earned after 13 years with this investment?
4. What if the investment was compounded monthly? What would the accumulated amount be?
5. How would the accumulated amount differ if the investment period was 20 years instead of 13?

**Tip:** When interest is compounded more frequently, the accumulated amount tends to be higher, even if the annual interest rate remains the same.

Learn how to calculate the accumulated amount $ A $ when a principal of $2200 is invested at an annual interest rate of 2% for 13 years, compounded semiannually. Follow our detailed solution using the compound interest formula. Rounded to the nearest cent.

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