Exact Interest Method
PRINCIPAL RATE TIME INTEREST
1 ₱ 810 7.5% ₱14.98
2 6% 105 DAYS ₱25.3
3 ₱11,400 5% 1 MONTH
4 ₱875 120 DAYS ₱17.26
5 ₱2,400 7% ₱23.01

To apply the **Exact Interest Method**, we use the following formula to calculate interest:

\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{365}
\]

Where:
- **Principal** = the initial amount of money.
- **Rate** = the annual interest rate (as a decimal).
- **Time** = the time period (in days) for which the interest is calculated.

Let's go through each case:

### 1. **Principal = ₱810, Rate = 7.5%, Interest = ₱14.98**

We need to find the **Time**.
\[
14.98 = 810 \times 0.075 \times \frac{\text{Time}}{365}
\]
Solve for Time:
\[
\frac{14.98}{810 \times 0.075} = \frac{\text{Time}}{365}
\]
\[
\text{Time} = \frac{14.98 \times 365}{810 \times 0.075} \approx 90.64 \, \text{days}
\]
Thus, the **Time** is approximately **91 days**.

### 2. **Rate = 6%, Time = 105 days, Interest = ₱25.30**

We need to find the **Principal**.
\[
25.30 = \text{Principal} \times 0.06 \times \frac{105}{365}
\]
Solve for Principal:
\[
\text{Principal} = \frac{25.30 \times 365}{0.06 \times 105} \approx ₱1,468.25
\]
Thus, the **Principal** is **₱1,468.25**.

### 3. **Principal = ₱11,400, Rate = 5%, Time = 1 month**

We need to find the **Interest**. Since we assume 1 month = 30 days:
\[
\text{Interest} = 11,400 \times 0.05 \times \frac{30}{365}
\]
\[
\text{Interest} \approx ₱46.85
\]
Thus, the **Interest** is **₱46.85**.

### 4. **Principal = ₱875, Time = 120 days, Interest = ₱17.26**

We need to find the **Rate**.
\[
17.26 = 875 \times \text{Rate} \times \frac{120}{365}
\]
Solve for Rate:
\[
\text{Rate} = \frac{17.26 \times 365}{875 \times 120} \approx 0.06
\]
Thus, the **Rate** is **6%**.

### 5. **Principal = ₱2,400, Rate = 7%, Interest = ₱23.01**

We need to find the **Time**.
\[
23.01 = 2,400 \times 0.07 \times \frac{\text{Time}}{365}
\]
Solve for Time:
\[
\text{Time} = \frac{23.01 \times 365}{2,400 \times 0.07} \approx 50.1 \, \text{days}
\]
Thus, the **Time** is approximately **50 days**.

---

Would you like more details or further clarification?

Here are 5 related questions to explore:
1. How does the exact interest method differ from the ordinary interest method?
2. How can we calculate interest for non-standard time periods, like weeks or months?
3. What is the impact of rounding on interest calculations in financial institutions?
4. Can you explain how the principal, time, and rate interact in compound interest?
5. How can you estimate interest for leap years?

**Tip:** Always double-check whether the time frame provided is based on a 360-day or 365-day year, as this can affect interest calculations.

Exact Interest Method: PRINCIPAL RATE TIME INTEREST 1 ₱810 7.5% ₱14.98 2 6% 105 DAYS ₱25.3 3 ₱11,400 5% 1 MONTH 4 ₱875 120 DAYS ₱17.26 5 ₱2,400 7% ₱23.01

Learn how to apply the Exact Interest Method to solve problems involving principal, rate, time, and interest. This guide covers detailed step-by-step solutions for calculating unknown values using the formula: Interest = Principal × Rate × (Time / 365). Suitable for students in Grades 9-12.

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