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.