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Let's solve the problems one by one using the simple interest formula:

\[
I = P \times r \times t
\]
Where:
- \(I\) is the interest,
- \(P\) is the principal (initial amount),
- \(r\) is the interest rate (in decimal form),
- \(t\) is the time (in years).

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

- Principal \(P = ₱6,200\),
- Rate \(r = 4\% = 0.04\),
- Time \(t = 1\) year.

\[
I = 6,200 \times 0.04 \times 1 = ₱248
\]

So, the interest earned is **₱248**.

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

To find the interest rate, we first calculate the interest earned:
\[
\text{Interest} = 41,070 - 27,750 = ₱13,320
\]

Now use the simple interest formula and solve for \(r\):
\[
I = P \times r \times t \implies r = \frac{I}{P \times t}
\]
\[
r = \frac{13,320}{27,750 \times 6} = \frac{13,320}{166,500} \approx 0.08
\]

So, the interest rate is **8%**.

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

We are given:
- Interest \(I = ₱2,520\),
- Principal \(P = ₱10,500\),
- Time \(t = 4\) years.

We use the same formula and solve for \(r\):
\[
r = \frac{I}{P \times t} = \frac{2,520}{10,500 \times 4} = \frac{2,520}{42,000} \approx 0.06
\]

So, the rate is **6%**.

---

Would you like further details or explanations on any of the problems?

Here are some related questions to think about:
1. How would the interest change if the rate in Problem 1 were 5% instead of 4%?
2. What would the total amount be for Problem 2 if the investment were over 10 years?
3. How much interest would be earned on ₱15,000 at 6% for 3 years?
4. How can we calculate the principal if we only know the interest, rate, and time?
5. How does compound interest differ from simple interest?

**Tip:** Always convert percentage rates to decimal form when calculating interest (e.g., 5% = 0.05).

1. How much interest is earned on ₱6,200 at 4% for one year? 2. What was the interest rate if your balance on an investment of ₱27,750 at the end of six years is ₱41,070? 3. At what rate was an investment made that obtains ₱2,520 on ₱10,500 over four years?

Solve word problems involving percentage rates related to simple interest. Learn how to calculate the interest earned on ₱6,200 at 4%, find the interest rate for an investment of ₱27,750 over six years, and determine the rate for an investment that earns ₱2,520 over four years.

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