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We are given a principal of $2000, a 5% interest rate compounded semiannually, and a period of 5 years. The goal is to calculate:

1. **The amount of money in the account after 5 years (A).**
2. **The amount of interest earned (B).**

### Step 1: Use the Compound Interest Formula
The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $A$ is the amount of money in the account after time $t$,
- $P$ is the principal amount ($2000),
- $r$ is the annual interest rate (5% or 0.05),
- $n$ is the number of times the interest is compounded per year (semiannually, so $n = 2$),
- $t$ is the number of years the money is invested or borrowed for (5 years).

### Step 2: Substitute the values
\[
A = 2000 \left(1 + \frac{0.05}{2}\right)^{2 \times 5}
\]
\[
A = 2000 \left(1 + 0.025\right)^{10}
\]
\[
A = 2000 (1.025)^{10}
\]

Let me calculate this for you.The amount of money in the account after 5 years is approximately **$2560.17**.

### Step 3: Calculate the Interest Earned
To find the interest earned, we subtract the initial principal from the total amount in the account:
\[
\text{Interest Earned} = A - P = 2560.17 - 2000
\]

Let me calculate this for you.The amount of interest earned over 5 years is approximately **$560.17**.

### Final Answers:
- **A.** The total amount in the account after 5 years is **$2560.17**.
- **B.** The interest earned is **$560.17**.

Would you like further clarification or details? Here are some related questions for practice:

1. What would be the total amount if the interest were compounded quarterly?
2. How does the time period affect the amount of interest earned?
3. What is the difference in the final amount if the interest rate was 6% instead of 5%?
4. How much interest would be earned if the account were only held for 3 years?
5. What would be the effect of continuous compounding on the total amount?

**Tip:** The more frequently interest is compounded, the greater the total amount will be, as interest accumulates more often!

Find how much money there will be in the account after 5 years, and calculate the interest earned with a principal of $2000 at a 5% interest rate compounded semiannually over 5 years.

Calculate the total amount and interest earned from a $2000 deposit over 5 years, at a 5% interest rate compounded semiannually. Learn the compound interest formula and step-by-step solution suitable for high school students.

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