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Let's analyze and solve the exercises step-by-step.

### Part A: Completing the Compound Interest Table

The table requires you to find unknown variables using the compound interest formula:
\[
A = P(1 + \frac{r}{n})^{nt}
\]
where:
- \( A \) = Maturity Value (Future Value),
- \( P \) = Principal,
- \( r \) = Rate of interest per period,
- \( n \) = Number of times interest is compounded per year,
- \( t \) = Time in years.

#### Table Analysis
1. **Row 1**: Known values are \( P = 6,000 \), \( r = 8\% \), \( t = 12 \) years. Use the formula to find the Maturity Value \( A \).
2. **Row 2**: Known values are \( P = 12,000 \), \( r = 5.5\% \), \( t = 6 \) years and 9 months. Convert 9 months to years (0.75 years) and solve for \( A \).
3. **Row 3**: Given \( P = 60,000 \), \( r = 9.75\% \), and \( t = 10 \) years. Find \( A \) using the compound interest formula.
4. **Row 4**: The Maturity Value \( A \) is 25,000, \( r = 6\% \), and \( t = 8 \) years. Use the formula to solve for \( P \), the principal.
5. **Row 5**: Given \( r = 7.5\% \), \( t = 4 \) years and 6 months (4.5 years), and Maturity Value \( A = 400,000 \). Solve for the principal \( P \).

I can calculate these if you'd like.

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### Part B: Compound Interest Word Problems

#### Problem Breakdown
1. **Problem 11**: Find how much Peter will owe after 2 years on a P100,000 loan at 8% compounded annually.
2. **Problem 12**: Calculate the interest earned on a P450,000 deposit at 5.5% compounded annually for 4 years.
3. **Problem 13**: Determine the investment amount needed to reach P250,000 in 5 years with a 12% compound interest rate.
4. **Problem 14**: Calculate the initial investment required to achieve P150,000 in 2 years at 10.5% interest compounded annually.
5. **Problem 15**: Find the amount that a student should deposit at 2% compounded annually to have P100,000 after 12 years.

Each of these problems can be solved using the compound interest formula or a variation, depending on the unknown variable.

Would you like me to calculate each value or provide guidance on specific problems? 

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#### Additional Questions

1. How does the compounding frequency (e.g., annually, semi-annually) impact the maturity value in compound interest?
2. If the interest rate increases, how does it affect the required principal to reach a certain maturity value within a fixed time frame?
3. How can we adjust the compound interest formula to account for different compounding intervals (e.g., quarterly)?
4. What is the difference in outcomes between simple interest and compound interest for the same principal, rate, and time?
5. How does a partial year (e.g., 9 months) affect the calculation of time in compound interest problems?

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#### Tip
Always convert the time into a consistent unit (years) when solving compound interest problems, especially when dealing with mixed months and years.

Solve the compound interest problems and fill in the missing values in the table provided in Lesson 25 Supplementary Exercises.

Solve compound interest problems and complete the missing values in a compound interest table. This lesson covers key concepts like principal, rate, time, and maturity value, using the compound interest formula to find unknowns. Suitable for high school students in Grades 10-12.

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