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Let's solve each of the three simple interest word problems step by step.

### Formula for Simple Interest:
The simple interest formula is:

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

Where:
- \( I \) = Interest
- \( P \) = Principal (initial investment)
- \( r \) = Interest rate (in decimal form)
- \( t \) = Time (in years)

---

### 1. **How much interest is earned on ₱6,200 at 4% for one year?**

We know:
- \( P = 6200 \)
- \( r = 4\% = 0.04 \)
- \( t = 1 \) year

Using the formula:

\[
I = 6200 \times 0.04 \times 1 = 248
\]

So, **₱248** is the interest earned.

---

### 2. **What was the interest rate if your balance on an investment of ₱27,750 at the end of six years is ₱41,070?**

We need to find the interest rate \( r \).

- Principal \( P = 27,750 \)
- Time \( t = 6 \) years
- Total balance at the end is ₱41,070, so the interest earned \( I \) is:

\[
I = 41,070 - 27,750 = 13,320
\]

Now use the simple interest formula and solve for \( r \):

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

\[
13,320 = 27,750 \times r \times 6
\]

Solve for \( r \):

\[
r = \frac{13,320}{27,750 \times 6} = 0.08 = 8\%
\]

The interest rate is **8%**.

---

### 3. **At what rate was an investment made that obtains ₱2,520 on ₱10,500 over four years?**

We need to find the interest rate \( r \).

- Principal \( P = 10,500 \)
- Interest \( I = 2,520 \)
- Time \( t = 4 \) years

Using the simple interest formula:

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

\[
2,520 = 10,500 \times r \times 4
\]

Solve for \( r \):

\[
r = \frac{2,520}{10,500 \times 4} = 0.06 = 6\%
\]

The interest rate is **6%**.

---

### Summary of Solutions:
1. ₱248 interest is earned on ₱6,200 at 4% for one year.
2. The interest rate was 8% for the investment that grew from ₱27,750 to ₱41,070 in six years.
3. The interest rate was 6% for an investment that earned ₱2,520 on ₱10,500 over four years.

Would you like further explanation or additional details on any of these problems?

Here are five related questions:
1. What is the total amount after 5 years if you invest ₱10,000 at an 8% simple interest rate?
2. How long would it take to double an investment at a 5% interest rate with simple interest?
3. What principal would yield ₱500 interest in 3 years at a 7% interest rate?
4. If you earned ₱300 in interest on an investment of ₱6,000 in 2 years, what was the interest rate?
5. How much interest will you earn on ₱15,000 at a rate of 9% over 4 years?

**Tip:** When working with percentages in interest problems, always convert the percentage to a decimal (e.g., 5% becomes 0.05) before using it in formulas.

Assessment: Read and solve each word problem involving percentage related to simple interest rate.

Learn how to solve simple interest word problems involving percentage calculations. This includes finding interest earned, determining the interest rate, and calculating the rate for investments over a specified time period. Suitable for students in Grades 6-8.

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