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

To find the interest rate on an investment, we can use the formula for compound interest or simple interest. Since you haven’t specified the type, let's assume it’s compound interest, which is the more common scenario for investments. The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \(A\) is the future value of the investment (₱41,070),
- \(P\) is the principal amount (₱27,750),
- \(r\) is the annual interest rate (which we need to find),
- \(n\) is the number of times the interest is compounded per year (if compounded annually, \(n = 1\)),
- \(t\) is the time the money is invested or borrowed for (6 years).

Since the compounding frequency is not mentioned, we'll assume it's compounded annually (\(n = 1\)).

Rearranging the formula to solve for \(r\):

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

Let me calculate the interest rate.The interest rate on the investment is approximately **6.75%** per year.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How does the interest rate change with different compounding periods?
2. What would the balance be after 10 years with the same interest rate?
3. How does compound interest compare to simple interest over 6 years?
4. What if the interest was compounded monthly instead of annually?
5. How can you calculate the present value of an investment with a future goal?

**Tip:** The frequency of compounding can significantly affect the final balance of an investment. The more frequently interest is compounded, the higher the balance will be.

Learn how to calculate the annual interest rate for an investment that grows from ₱27,750 to ₱41,070 over 6 years. This example uses the compound interest formula and assumes annual compounding, suitable for Grades 10-12 students.

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