Monika invests in a real estate project that earns 6.6% compounded semiannually. If her initial deposit is $10,000, how much interest will she earn if she keeps the investment for 7 years? 

To calculate how much interest Monika will earn, we can use the formula for compound interest:

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

Where:
- $ A $ = the amount of money after interest (final value)
- $ P $ = the principal (initial deposit), which is $10,000
- $ r $ = the annual interest rate (as a decimal), which is $ 6.6\% = 0.066 $
- $ n $ = the number of times the interest is compounded per year (semiannually, so $ n = 2 $)
- $ t $ = the time in years, which is 7 years

### Step 1: Calculate the total amount $ A $

\[
A = 10,000 \left(1 + \frac{0.066}{2}\right)^{2 \times 7}
\]

\[
A = 10,000 \left(1 + 0.033\right)^{14}
\]

\[
A = 10,000 \left(1.033\right)^{14}
\]

Now, I'll calculate the result.

\[
A = 10,000 \times 1.5583 \approx 15,583
\]

### Step 2: Calculate the interest earned

The interest earned is the total amount minus the principal:

\[
\text{Interest} = A - P = 15,583 - 10,000 = 5,583
\]

### Final Answer:
Monika will earn approximately **$5,583** in interest over 7 years.

Would you like further details or have any questions?

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Here are 5 related questions:
1. What would happen if the interest rate increased to 7%?
2. How much would Monika earn if the interest were compounded quarterly?
3. How does compounding annually compare with semiannually?
4. What if Monika withdraws her money after 5 years instead of 7?
5. How much total would she have if the rate were compounded monthly?

**Tip:** The more frequently interest is compounded, the more money you earn due to the "compounding effect."

Monika invests in a real estate project that earns 6.6% compounded semiannually. If her initial deposit is $10,000, how much interest will she earn if she keeps the investment for 7 years?

Learn how to calculate the interest earned on a $10,000 investment with a 6.6% interest rate compounded semiannually over 7 years. This detailed solution uses the compound interest formula to find the total amount and the interest earned, suitable for students in Grades 9-12.

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