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.

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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.