To find the interest rate for an investment, we can use the formula for compound interest:

$A = P(1 + r)^t$

Where:

• $A$ is the final amount (₱41,070),
• $P$ is the initial principal (₱27,750),
• $r$ is the annual interest rate (which we are solving for),
• $t$ is the time in years (6 years).

We can rearrange the formula to solve for $r$:

$r = \left( \frac{A}{P} \right)^{\frac{1}{t}} - 1$

Now, let's calculate the interest rate.

$r = \left( \frac{41,070}{27,750} \right)^{\frac{1}{6}} - 1$

Let me compute that for you.The annual interest rate for the investment is approximately 6.75%.

Would you like further details or explanations on this calculation?

Here are some related questions for further exploration:

1. What would the interest rate be if the investment period was 10 years?
2. How much would the balance be after 8 years with the same interest rate?
3. How does the interest rate change if the final balance was ₱50,000 instead?
4. What would the interest rate be if the initial investment was ₱30,000?
5. How does the interest rate differ for simple vs compound interest?

Tip: Always ensure to verify if the interest being applied is simple or compound, as it significantly affects the final amount.