Find the ordinary and exact interest at 6% for 120 days on a.)₱11500 b.)₱ 15000 c.)₱20000 show me the solution

To find the ordinary and exact interest for each principal amount at an interest rate of 6% over 120 days, we can use the formulas for simple interest. The difference between ordinary interest and exact interest lies in how the number of days in a year is calculated.

### Formulas:
1. **Ordinary Interest (360-day year):**
   \[
   I_{\text{ordinary}} = P \times r \times \frac{t}{360}
   \]
   
2. **Exact Interest (365-day year):**
   \[
   I_{\text{exact}} = P \times r \times \frac{t}{365}
   \]

Where:
- \( P \) is the principal amount.
- \( r \) is the annual interest rate (as a decimal).
- \( t \) is the time in days.

### Calculations:
Given:
- Interest rate (\( r \)) = 6% = 0.06
- Time (\( t \)) = 120 days

#### a.) ₱11,500

1. **Ordinary Interest:**
   \[
   I_{\text{ordinary}} = 11500 \times 0.06 \times \frac{120}{360} = 11500 \times 0.06 \times 0.3333 = 229.98
   \]

2. **Exact Interest:**
   \[
   I_{\text{exact}} = 11500 \times 0.06 \times \frac{120}{365} = 11500 \times 0.06 \times 0.3288 = 226.86
   \]

#### b.) ₱15,000

1. **Ordinary Interest:**
   \[
   I_{\text{ordinary}} = 15000 \times 0.06 \times \frac{120}{360} = 15000 \times 0.06 \times 0.3333 = 300
   \]

2. **Exact Interest:**
   \[
   I_{\text{exact}} = 15000 \times 0.06 \times \frac{120}{365} = 15000 \times 0.06 \times 0.3288 = 296.55
   \]

#### c.) ₱20,000

1. **Ordinary Interest:**
   \[
   I_{\text{ordinary}} = 20000 \times 0.06 \times \frac{120}{360} = 20000 \times 0.06 \times 0.3333 = 400
   \]

2. **Exact Interest:**
   \[
   I_{\text{exact}} = 20000 \times 0.06 \times \frac{120}{365} = 20000 \times 0.06 \times 0.3288 = 395.40
   \]

### Summary of Results:
1. **₱11,500**
   - Ordinary Interest: ₱229.98
   - Exact Interest: ₱226.86

2. **₱15,000**
   - Ordinary Interest: ₱300.00
   - Exact Interest: ₱296.55

3. **₱20,000**
   - Ordinary Interest: ₱400.00
   - Exact Interest: ₱395.40

Would you like more details or have any questions?

### Related Questions:
1. What is the difference between ordinary interest and exact interest?
2. How does the length of time affect the amount of interest accrued?
3. What is the effect of different interest rates on the same principal amount?
4. How would the interest change if the time period was 90 days instead of 120 days?
5. How does compounding differ from simple interest?

### Tip:
Always double-check the number of days used in the calculation, especially when determining whether to use a 360-day or 365-day year.

Learn how to calculate ordinary and exact interest at a 6% rate for different principal amounts over 120 days. Understand the difference between ordinary and exact interest calculations using the formulas for simple interest. Suitable for high school students and anyone interested in financial calculations.

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