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Let's go over the questions shown in the image:

### 1. **How long will it take ₱15,000 to earn ₱5,000 if it is invested at 12% monthly?**

This is a compound interest problem. The goal is to find the time it takes for ₱15,000 to grow to ₱20,000 (since ₱15,000 + ₱5,000 = ₱20,000) at a monthly interest rate of 12%. 

We can use the compound interest formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A\) is the future value (₱20,000),
- \(P\) is the principal amount (₱15,000),
- \(r\) is the annual interest rate (12% monthly would be \(12 \times 12 = 144\%\)),
- \(n\) is the number of times the interest is compounded per year (monthly, so \(n = 12\)),
- \(t\) is the time in years.

We can solve for \(t\).

---

### 2. **Norra borrowed ₱40,000 which she paid with an interest of ₱2,000 at the end of 3 years. At what nominal rate compounded semi-annually was it invested?**

This is another compound interest problem, but this time we need to find the interest rate. The interest earned is ₱2,000, so the total amount paid is ₱42,000. 

We can use the formula again:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A = 42,000\),
- \(P = 40,000\),
- \(t = 3\) years,
- \(n = 2\) (since it's compounded semi-annually),
- and we solve for \(r\), the nominal rate.

Would you like me to proceed with the calculations and explanations for both questions?

1. How long will it take ₱15,000 to earn ₱5,000 if it is invested at 12% monthly? 2. Norra borrowed an amount of ₱40,000 which she paid with an interest of ₱2,000 at the end of 3 years. At what nominal rate compounded semi-annually was it invested?

Learn how to calculate the time it takes for ₱15,000 to grow to ₱20,000 with monthly compound interest at 12%, and find the nominal rate for a ₱40,000 loan paid with ₱2,000 interest after 3 years, compounded semi-annually.

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