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The question involves calculating compound interest based on the provided formula:

\[
B = p(1 + r)^t
\]

Where:
- $ B $ is the balance (final amount),
- $ p = 7,000 $ is the principal (initial deposit),
- $ r = 0.15 $ is the interest rate (15% as a decimal),
- $ t = 3 $ years is the time.

We are tasked with finding how much interest Derek will earn in 3 years.

### Step 1: Calculate the final amount $ B $
\[
B = 7000 \times (1 + 0.15)^3
\]
\[
B = 7000 \times (1.15)^3
\]
\[
B = 7000 \times 1.520875
\]
\[
B = 10,646.13
\]

### Step 2: Calculate the interest earned
The interest is the difference between the final amount and the principal:
\[
\text{Interest} = B - p
\]
\[
\text{Interest} = 10,646.13 - 7,000
\]
\[
\text{Interest} = 3,646.13
\]

Derek will earn **$3,646.13** in interest over 3 years.

Would you like more details on any step? 

Here are five related questions for further practice:
1. What would be the interest if the rate were 10% instead of 15%?
2. How much would Derek earn in 5 years at the same rate?
3. What if the interest were compounded semi-annually instead of annually?
4. How would the result change if the principal were $10,000 instead of $7,000?
5. What is the effect of a 2-year deposit instead of 3 years?

**Tip:** The higher the interest rate or the longer the time period, the more significant the effect of compound interest on growth!

Derek deposited $7,000 in an account earning 15% interest compounded annually. To the nearest cent, how much interest will he earn in 3 years? Use the formula B = p(1 + r)^t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Learn how to calculate compound interest for a $7,000 deposit at a 15% interest rate compounded annually over 3 years. This problem includes step-by-step calculations using the compound interest formula, ideal for students in Grades 9-11.

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