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Let's solve the two math problems in the image:

### 14. Angeline borrowed ₱15,000.00 and paid back ₱16,800.00 at the end of 3 years. What is the simple interest rate given to Angeline?

We can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- \( I \) is the interest paid,
- \( P \) is the principal (₱15,000.00),
- \( r \) is the interest rate,
- \( t \) is the time (3 years).

First, calculate the interest \( I \):

\[
I = 16,800 - 15,000 = 1,800
\]

Now, using the formula for simple interest, solve for \( r \):

\[
r = \frac{I}{P \times t} = \frac{1,800}{15,000 \times 3}
\]

Now, calculating:

\[
r = \frac{1,800}{45,000} = 0.04 = 4\%
\]

So, the simple interest rate given to Angeline is **4% per year**.

---

### 15. How much money was borrowed by Leia 4 years ago, if at present she paid a total of ₱31,000.00 at a simple interest rate of 6% per year?

We need to determine the principal \( P \) using the formula:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the total amount paid (₱31,000),
- \( r \) is the interest rate (6% or 0.06),
- \( t \) is the time (4 years),
- \( P \) is the principal we need to find.

Substitute the known values into the formula:

\[
31,000 = P(1 + 0.06 \times 4)
\]

\[
31,000 = P(1 + 0.24) = P(1.24)
\]

Solve for \( P \):

\[
P = \frac{31,000}{1.24} \approx 25,000
\]

So, Leia borrowed **₱25,000.00** 4 years ago.

---

Would you like further details or have any questions about these problems?

Here are five related questions you can explore:
1. What is the formula for compound interest, and how does it differ from simple interest?
2. If Angeline had taken the loan for 5 years instead of 3, what would have been her total repayment at the same interest rate?
3. If Leia had borrowed the same amount but at an 8% simple interest rate, what would her total repayment be?
4. How does changing the time period of a loan affect the total interest paid under simple interest?
5. What happens if Leia makes partial repayments during the loan period—how does that affect the total interest?

**Tip:** When solving for interest rates or principal, always make sure to carefully arrange the equation before calculating to avoid mistakes.

14. Angeline borrowed ₱15,000.00 and paid back ₱16,800.00 at the end of 3 years. What is the simple interest rate given to Angeline? 15. How much money was borrowed by Leia 4 years ago, if at present she paid a total of ₱31,000.00 at a simple interest rate of 6% per year?

Learn how to calculate simple interest and loan repayments through examples. Angeline borrows ₱15,000 and repays ₱16,800 after 3 years, and Leia repays ₱31,000 after 4 years at 6% interest. Detailed step-by-step solutions provided.

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