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

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

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

Where:
- \( A \) is the final amount (₱41,070),
- \( P \) is the principal or initial amount (₱27,750),
- \( r \) is the annual interest rate (what we are solving for),
- \( t \) is the time in years (6 years).

We will solve for \( r \).

### Step 1: Substitute the known values into the formula
\[
41,070 = 27,750 \left( 1 + r \right)^6
\]

### Step 2: Solve for \( (1 + r)^6 \)
\[
\frac{41,070}{27,750} = \left( 1 + r \right)^6
\]

\[
1.47913 \approx \left( 1 + r \right)^6
\]

### Step 3: Take the 6th root of both sides
\[
1 + r = \left( 1.47913 \right)^{\frac{1}{6}}
\]

\[
1 + r \approx 1.06605
\]

### Step 4: Solve for \( r \)
\[
r \approx 1.06605 - 1
\]

\[
r \approx 0.06605
\]

Thus, the annual interest rate is approximately **6.61%**.

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

Here are 5 related questions for further exploration:
1. What would the balance be after 10 years at the same interest rate?
2. How would the interest rate change if the final amount was ₱50,000?
3. What is the difference between compound interest and simple interest?
4. How can you calculate the time needed to reach a certain amount with a fixed interest rate?
5. What impact does compounding frequency (annual, semi-annual, etc.) have on the interest rate?

**Tip:** When calculating interest over several years, compound interest grows faster than simple interest, as it includes interest on previously earned interest!

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 that grows from ₱27,750 to ₱41,070 over six years using the compound interest formula. This solution is ideal for students in Grades 9-12 and covers key concepts in finance and exponential growth.

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