Alright, everyone! Today, we'll tackle compound interest problems step-by-step using Polya's method and answer the 3Cs questions - Concerns, Connections, and Considerations, based on the given problem.

1. Pedro, a farmer, wants to expand his farm and needs a loan from NMAPMC. He plans to borrow PHP
150,000 to purchase additional land and equipment. NMAPMC offers loans at an annual interest rate of
12%, compounded annually. Pedro wants to know how much he will owe at the end of a 3-year loan term.
Solution:
I. Understand the problem:
II. Make a plan:
Ill. Carry out the plan:

Let's work through the compound interest problem Pedro is facing, using Polya's four-step problem-solving method. We'll also address the 3Cs—Concerns, Connections, and Considerations—to thoroughly analyze the problem.

### Problem Overview
Pedro, a farmer, needs to borrow PHP 150,000 at a 12% annual interest rate compounded annually for a 3-year term. The goal is to determine how much he will owe at the end of this 3-year loan term.

### Step-by-Step Solution using Polya's Method:

---

### **I. Understand the Problem:**
We need to calculate how much Pedro will owe after 3 years of borrowing PHP 150,000 at an annual interest rate of 12%, compounded annually. 

This is a **compound interest problem** where the amount owed includes interest that is added back into the principal, which then earns interest itself in subsequent years.

The formula for compound interest is:

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

Where:
- \(A\) = the amount after interest (what Pedro will owe)
- \(P\) = principal (the initial amount) = PHP 150,000
- \(r\) = annual interest rate = 12% = 0.12
- \(n\) = number of times the interest is compounded per year = 1 (since it's compounded annually)
- \(t\) = the time the money is borrowed for (in years) = 3 years

---

### **II. Make a Plan:**
Our plan is to apply the **compound interest formula** to find the total amount Pedro will owe after 3 years. The formula simplifies since the interest is compounded annually (\(n = 1\)).

The simplified formula becomes:

\[
A = P \left( 1 + r \right)^t
\]

Now, we'll plug in the known values:
- \(P = 150,000\)
- \(r = 0.12\)
- \(t = 3\)

---

### **III. Carry Out the Plan:**

Let’s substitute the values into the simplified compound interest formula:

\[
A = 150,000 \left( 1 + 0.12 \right)^3
\]

First, calculate \(1 + 0.12 = 1.12\), then raise this to the power of 3:

\[
A = 150,000 \times (1.12)^3
\]

Now calculate \(1.12^3\):

\[
1.12^3 = 1.404928
\]

So:

\[
A = 150,000 \times 1.404928
\]

Finally, multiply to get the total amount:

\[
A = 210,739.20
\]

Thus, at the end of 3 years, Pedro will owe **PHP 210,739.20**.

---

### **IV. Review and Reflect:**

Pedro will owe PHP 210,739.20 at the end of the 3-year loan term. This amount includes both the principal and the interest accumulated over the 3 years.

---

### 3Cs: Concerns, Connections, and Considerations

- **Concerns**: Pedro should ensure he can repay PHP 210,739.20 after 3 years. Can his farm's expansion generate enough income to cover this repayment?
- **Connections**: Compound interest appears in many financial situations, including savings accounts and mortgages. Pedro’s loan terms are similar to those of other loans offered by banks.
- **Considerations**: Pedro might want to explore other loan options that offer a lower interest rate or different compounding frequencies (e.g., monthly compounding) to reduce the total amount owed.

---

### Questions:
1. What would Pedro owe if the interest rate were 10% instead of 12%?
2. How does changing the compounding frequency (e.g., monthly compounding) affect the amount owed?
3. What is the total interest Pedro will pay after 3 years?
4. If Pedro repays part of the loan early, how would that affect the total owed?
5. How would Pedro’s total loan amount change if he took out a loan for 5 years instead of 3 years?

### Tip:
When dealing with loans or investments, always consider the compounding frequency—more frequent compounding leads to more interest!

Alright, everyone! Today, we'll tackle compound interest problems step-by-step using Polya's method and answer the 3Cs questions - Concerns, Connections, and Considerations, based on the given problem.

1. Pedro, a farmer, wants to expand his farm and needs a loan from NMAPMC. He plans to borrow PHP 150,000 to purchase additional land and equipment. NMAPMC offers loans at an annual interest rate of 12%, compounded annually. Pedro wants to know how much he will owe at the end of a 3-year loan term.

Learn how to calculate the total amount owed on a PHP 150,000 loan over 3 years with an annual interest rate of 12%, compounded annually. This problem uses Polya's method to solve compound interest problems and explores Concerns, Connections, and Considerations. Suitable for Grades 10-12 students.

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