What was the interest rate if your balance on an invesment of pesos 27750 at the end of six years pesos 41070

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.

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

Learn how to calculate the annual interest rate for an investment of ₱27,750 that grows to ₱41,070 over 6 years using the compound interest formula. Explore key concepts like exponential growth and apply the formula step by step. Suitable for students in Grades 10-12.

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