If P45,000 accumulates to P105,000 invested in 12 years, what is the interest rate?

To find the interest rate for an investment that grows from P45,000 to P105,000 over 12 years, we can use the formula for compound interest or the formula for simple interest, depending on the context. Since the problem doesn't specify whether the interest is compounded or simple, I'll assume simple interest for this example.

### Simple Interest Formula
The simple interest formula is:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the final amount (P105,000),
- \( P \) is the principal amount (P45,000),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years (12 years).

Substituting the known values:

\[
105,000 = 45,000(1 + 12r)
\]

### Solving for \( r \):

1. Divide both sides by 45,000:
   \[
   \frac{105,000}{45,000} = 1 + 12r
   \]

   \[
   2.\overline{3} = 1 + 12r
   \]

2. Subtract 1 from both sides:
   \[
   1.\overline{3} = 12r
   \]

3. Divide by 12:
   \[
   r = \frac{1.\overline{3}}{12}
   \]

   \[
   r = \frac{4}{36} = \frac{1}{9} \approx 0.1111
   \]

### Final Answer
The interest rate is approximately \( 0.1111 \) or **11.11%** per year.

Would you like further details or have any other questions?

Here are some related questions you might find useful:

1. How would the interest rate change if the investment period was 10 years instead of 12?
2. What would the accumulated amount be if the interest rate was 15%?
3. How does compound interest differ from simple interest in this context?
4. How can I calculate the future value of an investment with compound interest?
5. What is the formula for calculating continuous compounding interest?

**Tip:** When solving for an unknown interest rate, always check whether the problem involves simple or compound interest, as the formulas differ.

Learn how to calculate the interest rate when an investment grows from P45,000 to P105,000 over 12 years. This problem involves using the simple interest formula to find the annual rate. Suitable for high school students and anyone interested in financial mathematics.

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