3. Find the ordinary interest and final amount on P15,000 for 90 days at: a) 51 and 1 fourth% b) 12% c) 12.75% 4. Find the ordinary interest and exact interest at 7% on 9,500 and the corresponding amount at the end of 100 days. (Answer must be round off to the nearest centavo)

Let's solve each part step by step.

### Problem 3: Ordinary Interest and Final Amount
We'll use the formula for **ordinary interest**:
\[
I = \frac{P \times r \times t}{360}
\]
where:
- \( P \) is the principal amount
- \( r \) is the annual interest rate (as a decimal)
- \( t \) is the time period in days

The **final amount** (A) is then:
\[
A = P + I
\]

#### Part a) 51 and 1/4% (which is 51.25%)
- \( P = 15,000 \) 
- \( r = 0.5125 \)
- \( t = 90 \)

\[
I_a = \frac{15,000 \times 0.5125 \times 90}{360} 
\]

\[
I_a = \frac{15,000 \times 0.5125 \times 90}{360} = 1,922.81 \text{ (rounded to the nearest centavo)}
\]
\[
A_a = 15,000 + 1,922.81 = 16,922.81
\]

#### Part b) 12%
- \( P = 15,000 \) 
- \( r = 0.12 \)
- \( t = 90 \)

\[
I_b = \frac{15,000 \times 0.12 \times 90}{360} 
\]

\[
I_b = \frac{15,000 \times 0.12 \times 90}{360} = 450
\]
\[
A_b = 15,000 + 450 = 15,450
\]

#### Part c) 12.75%
- \( P = 15,000 \)
- \( r = 0.1275 \)
- \( t = 90 \)

\[
I_c = \frac{15,000 \times 0.1275 \times 90}{360}
\]

\[
I_c = \frac{15,000 \times 0.1275 \times 90}{360} = 478.13 \text{ (rounded to the nearest centavo)}
\]
\[
A_c = 15,000 + 478.13 = 15,478.13
\]

### Problem 4: Ordinary and Exact Interest
Let's find both the **ordinary interest** and **exact interest** on \( P = 9,500 \) at 7% over 100 days.

#### Ordinary Interest:
Using the formula:
\[
I_o = \frac{P \times r \times t}{360}
\]

\[
I_o = \frac{9,500 \times 0.07 \times 100}{360} 
\]

\[
I_o = 184.72 \text{ (rounded to the nearest centavo)}
\]

Final amount:
\[
A_o = 9,500 + 184.72 = 9,684.72
\]

#### Exact Interest:
Exact interest is calculated using 365 days instead of 360 days:
\[
I_e = \frac{P \times r \times t}{365}
\]

\[
I_e = \frac{9,500 \times 0.07 \times 100}{365}
\]

\[
I_e = 182.19 \text{ (rounded to the nearest centavo)}
\]

Final amount:
\[
A_e = 9,500 + 182.19 = 9,682.19
\]

### Summary of Results:

**Problem 3:**
- **a)** Interest: ₱1,922.81, Final Amount: ₱16,922.81
- **b)** Interest: ₱450, Final Amount: ₱15,450
- **c)** Interest: ₱478.13, Final Amount: ₱15,478.13

**Problem 4:**
- **Ordinary Interest:** ₱184.72, Final Amount: ₱9,684.72
- **Exact Interest:** ₱182.19, Final Amount: ₱9,682.19

Would you like to go over the steps in more detail or have any questions?

---

**Related Questions:**
1. How is exact interest different from ordinary interest?
2. What would be the interest for a 365-day period for problem 3c?
3. How does compounding interest differ from simple interest?
4. What are the benefits of calculating exact interest over ordinary interest?
5. How would the interest change if the time was 180 days instead of 90 in problem 3?

**Tip:** Always double-check whether to use a 360-day or 365-day basis when calculating interest, as it can significantly affect the results.

Learn how to calculate ordinary and exact interest on principal amounts using simple interest formulas. Includes examples for different interest rates and time periods. Suitable for high school students and learners of finance.

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