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 solve these interest problems using the Exact Interest Method, the formula for simple interest is:

\[
I = P \times r \times t
\]

Where:
- \( I \) = Interest
- \( P \) = Principal
- \( r \) = Interest rate (annual, in decimal form)
- \( t \) = Time in years (with days converted based on the actual days of the year: 365 or 366)

Let's calculate each one based on the given information.

### Problem 1:
Given:
- \( P = ₱810 \)
- \( r = 7.5\% = 0.075 \)
- \( I = ₱14.98 \)

We can find \( t \) by rearranging the formula:

\[
t = \frac{I}{P \times r} = \frac{14.98}{810 \times 0.075}
\]

Let's calculate \( t \).

### Problem 2:
Given:
- \( r = 6\% = 0.06 \)
- \( t = 105 \text{ days} = \frac{105}{365} \text{ years} \)
- \( I = ₱25.3 \)

We can find \( P \) by rearranging the formula:

\[
P = \frac{I}{r \times t} = \frac{25.3}{0.06 \times \frac{105}{365}}
\]

### Problem 3:
Given:
- \( P = ₱11,400 \)
- \( r = 5\% = 0.05 \)
- \( t = 1 \text{ month} = \frac{30}{365} \text{ years} \)

We can calculate \( I \) by plugging values into the formula:

\[
I = P \times r \times t = 11,400 \times 0.05 \times \frac{30}{365}
\]

### Problem 4:
Given:
- \( P = ₱875 \)
- \( t = 120 \text{ days} = \frac{120}{365} \text{ years} \)
- \( I = ₱17.26 \)

We can find \( r \) by rearranging the formula:

\[
r = \frac{I}{P \times t} = \frac{17.26}{875 \times \frac{120}{365}}
\]

### Problem 5:
Given:
- \( P = ₱2,400 \)
- \( r = 7\% = 0.07 \)
- \( I = ₱23.01 \)

We can find \( t \) by rearranging the formula:

\[
t = \frac{I}{P \times r} = \frac{23.01}{2400 \times 0.07}
\]

Let me calculate the unknowns.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can walk you through solving the calculations manually or explain the concepts further.

Here are some related questions to expand your understanding:
1. How do you convert interest rates to decimals?
2. Why is the number of days in the year important in the exact interest method?
3. Can the Exact Interest Method be used for compound interest?
4. How would the formula change if the time period were expressed in months rather than days?
5. What are some other methods of calculating interest besides the Exact Interest Method?

**Tip:** Always double-check your conversions (e.g., days to years) to avoid calculation errors.

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 solve problems using the Exact Interest Method with the formula I = P × r × t. This step-by-step guide covers calculating principal, rate, time, and interest for various problems involving time periods in days and months. Suitable for students in Grades 9-12.

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