Suppose that $15,000 is deposited for five years at 4% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.


To solve this problem, we will use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after interest.
- $ P = 15,000 $ is the initial principal (deposit).
- $ r = 0.04 $ is the annual interest rate (4% APR).
- $ n = 2 $ because the interest is compounded semiannually (2 times per year).
- $ t = 5 $ years is the time the money is invested for.

### Step-by-Step Calculation:
1. **Substitute the known values into the formula**:
\[
A = 15000 \left(1 + \frac{0.04}{2}\right)^{2 \times 5}
\]
\[
A = 15000 \left(1 + 0.02\right)^{10}
\]
\[
A = 15000 \left(1.02\right)^{10}
\]

2. **Calculate $ (1.02)^{10} $**:
\[
1.02^{10} \approx 1.21899
\]

3. **Multiply by the principal**:
\[
A \approx 15000 \times 1.21899 = 18284.85
\]

4. **Calculate the interest earned**:
\[
\text{Interest} = A - P = 18284.85 - 15000 = 3284.85
\]

Thus, the interest earned after 5 years is approximately **$3,284.85**.

Would you like further details or explanations?

Here are 5 related questions to explore:
1. How does the frequency of compounding affect interest earned?
2. What would happen if the interest were compounded quarterly instead?
3. What is the difference between simple interest and compound interest?
4. How would the interest change if the APR were 5% instead of 4%?
5. Can you calculate the future value if the money was left for 10 years?

**Tip:** Compound interest grows faster when the frequency of compounding increases!

Suppose that $15,000 is deposited for five years at 4% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.

Find out how to calculate the interest earned on $15,000 deposited for five years at 4% APR, compounded semiannually. This detailed step-by-step solution explores the compound interest formula and demonstrates how compounding affects interest growth. Perfect for high school students in Grades 9-12.

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