Find the interest for a 3-year CD for $5,000 at an interest rate of 2.5%, compounded annually.

To find the interest for a certificate of deposit (CD) compounded annually, we can 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 (initial deposit), which is $5,000.
- $ r $ is the annual interest rate, which is 2.5% or 0.025 in decimal form.
- $ n $ is the number of times interest is compounded per year, which is 1 for annual compounding.
- $ t $ is the time the money is invested for, which is 3 years.

#### Step 1: Plug in the values
\[
A = 5000 \left(1 + \frac{0.025}{1}\right)^{1 \times 3}
\]

#### Step 2: Simplify inside the parentheses
\[
A = 5000 \left(1 + 0.025\right)^3
\]
\[
A = 5000 \times (1.025)^3
\]

#### Step 3: Calculate $ (1.025)^3 $
\[
(1.025)^3 \approx 1.0769
\]

#### Step 4: Find the final amount $ A $
\[
A \approx 5000 \times 1.0769 = 5384.50
\]

#### Step 5: Calculate the interest earned
\[
\text{Interest} = A - P = 5384.50 - 5000 = 384.50
\]

### Answer
The interest earned after 3 years is approximately **$384.50**.

Would you like a detailed breakdown of each step or have any questions? 

Here are some related questions:
1. What is the difference in interest if compounding is done quarterly instead of annually?
2. How would the interest change if the rate was 3% instead of 2.5%?
3. How would the total interest differ for a CD of 5 years instead of 3 years?
4. What happens to the total interest if the initial amount was $10,000?
5. How do you calculate compound interest if the compounding period is monthly?

**Tip:** Always double-check if the compounding period (annually, quarterly, monthly) matches the given problem to ensure correct calculations.

Learn to calculate the interest on a 3-year certificate of deposit (CD) with a $5,000 principal and 2.5% interest rate, compounded annually. Follow a detailed step-by-step solution using the compound interest formula, ideal for high school students.

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