What was the interest rate if your balance on an investment of P27,750 at the end of six years is P41,070?

To find the interest rate, we can use the **compound interest formula**:

\[
A = P(1 + r)^t
\]

Where:
- \(A\) is the amount of money after interest (final balance), which is \(P41,070\),
- \(P\) is the principal or initial investment, which is \(P27,750\),
- \(r\) is the interest rate (what we need to find),
- \(t\) is the time in years, which is 6 years.

We can rearrange the formula to solve for \(r\):

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

Now, let's substitute the known values:

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

I'll calculate this for you.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can easily compute the interest rate manually using the formula I provided:

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

This will give you the interest rate. If you need further help or another question answered, feel free to ask.

Would you like more details, or do you have any other questions?

Here are 5 related questions to expand on this topic:
1. What is the formula for calculating simple interest?
2. How does compound interest differ from simple interest?
3. How can you calculate the future value of an investment with continuous compounding?
4. What factors influence the growth of an investment over time?
5. How does the frequency of compounding affect the final amount of an investment?

**Tip**: Knowing the difference between simple and compound interest is crucial when evaluating long-term investments!

Learn how to calculate the interest rate on an investment of P27,750 over six years, yielding a final balance of P41,070. This solution uses the compound interest formula and is suitable for students in Grades 10-12. A step-by-step approach to finding the interest rate is provided.

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