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Let's solve the two problems presented in the image.

### 1. Interest and Maturity Value of a Loan
The formula for simple interest is:
\[
I = P \times r \times t
\]
Where:
- \( I \) = Interest
- \( P \) = Principal amount = 33,000 PHP
- \( r \) = Annual interest rate = 12.5% = 0.125
- \( t \) = Time in years = 5 years

Now, calculate the interest:
\[
I = 33,000 \times 0.125 \times 5 = 20,625 \, \text{PHP}
\]

The maturity value (\( A \)) is the total amount after the interest is added:
\[
A = P + I = 33,000 + 20,625 = 53,625 \, \text{PHP}
\]

Thus, the interest is **20,625 PHP**, and the maturity value is **53,625 PHP**.

---

### 2. Finding Interest Rate and Time
#### Part A: At what simple interest per annum will \( P_1 \) become \( P_2 \) in 2 years?
This part asks for the rate at which an initial principal \( P_1 \) becomes \( P_2 \) after 2 years. The simple interest formula rearranged for rate (\( r \)) is:
\[
r = \frac{P_2 - P_1}{P_1 \times t}
\]
Since no specific values for \( P_1 \) and \( P_2 \) are given, we keep the formula general for now.

#### Part B: How long for 1 million pesos to earn 100,000 PHP at 3% per annum?
Here, \( P = 1,000,000 \) PHP, \( I = 100,000 \) PHP, and \( r = 3\% = 0.03 \). The formula for time is:
\[
t = \frac{I}{P \times r}
\]

Substitute the known values:
\[
t = \frac{100,000}{1,000,000 \times 0.03} = \frac{100,000}{30,000} \approx 3.33 \, \text{years}
\]

So, it will take approximately **3.33 years** to earn 100,000 PHP in interest.

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Would you like more details on any of these solutions or have other questions? Here are 5 related questions:

1. How is compound interest different from simple interest?
2. How would the calculation change if the loan period were in months rather than years?
3. What happens to the interest if the rate changes midway through the loan period?
4. Can you calculate the interest if the principal grows over time (e.g., through additional deposits)?
5. How can inflation affect the real value of the maturity amount?

**Tip:** Always double-check if the interest rate provided is annual, and adjust the formula accordingly if the time is given in months or days.

1. What are the amounts of interest and maturity value of a loan for PHP 33,000 at 12.5% simple interest for 5 years? 2. At what simple interest per annum will P1 become P2 in 2 years? How long will 1 million pesos earn a simple interest of PHP 100,000 at 3% per annum?

Learn how to calculate the interest and maturity value of a loan of PHP 33,000 at 12.5% simple interest for 5 years, and how long it will take to earn PHP 100,000 from 1 million pesos at 3% per annum. This covers key formulas like the simple interest formula and time calculation.

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