On May  
8
8,  
2015
2015, Mrs. Siega borrowed  
₱
500
,
000
₱500,000  from Mr. Singh at  
3
%
3%  payable in  
120
120  days. If this amount is equivalent to  
3
%
3%  in a bank, find its present value on July  
6
6,  
2015
2015.

We are tasked with finding the present value of ₱500,000, borrowed on May 8, 2015, at 3% interest, payable in 120 days, and we need to find its present value on July 6, 2015.

### Step-by-Step Breakdown

1. **Identify Key Information**:
   - Principal: ₱500,000
   - Interest Rate: 3% annually
   - Time Period: 120 days
   - Present Value Date: July 6, 2015
   - Loan Date: May 8, 2015

2. **Days between May 8, 2015, and July 6, 2015**:
   First, we need to count the number of days between May 8 and July 6:
   - From May 8 to May 31 = 24 days
   - June = 30 days
   - July 1 to July 6 = 6 days
   
   Total days = 24 + 30 + 6 = **60 days**

3. **Determine the Remaining Days**:
   The loan is due in 120 days, so from July 6, there are \(120 - 60 = 60\) days remaining.

4. **Apply the Present Value Formula**:
   The present value (PV) can be calculated using the formula:

   \[
   PV = \frac{F}{1 + \frac{r \cdot t}{360}}
   \]
   Where:
   - \( F \) is the future value (₱500,000)
   - \( r \) is the annual interest rate (3% or 0.03)
   - \( t \) is the time in days (60 days remaining)
   - 360 is the number of days used in financial calculations (banker's rule)

   Substituting the values:

   \[
   PV = \frac{500,000}{1 + \frac{0.03 \cdot 60}{360}}
   \]

5. **Solve**:
   First, calculate the interest factor:

   \[
   \frac{0.03 \cdot 60}{360} = 0.005
   \]

   Now, calculate the denominator:

   \[
   1 + 0.005 = 1.005
   \]

   Finally, calculate the present value:

   \[
   PV = \frac{500,000}{1.005} = 497,512.44
   \]

### Result:
The present value of ₱500,000 on July 6, 2015, is **₱497,512.44**.

Would you like further details or explanations on any step?

### Related Questions:
1. What is the formula for calculating the future value from a present value?
2. How does changing the interest rate affect the present value of a loan?
3. Can the number of days used in the calculation vary between countries or banks?
4. How would the present value change if the loan was compounded monthly?
5. What is the difference between simple and compound interest when calculating loan repayments?

### Tip:
Always ensure you correctly identify the time remaining and the proper interest rate when calculating present values for different dates.

On May 8, 2015, Mrs. Siega borrowed ₱500,000 from Mr. Singh at 3% payable in 120 days. If this amount is equivalent to 3% in a bank, find its present value on July 6, 2015.

Learn how to calculate the present value of a ₱500,000 loan borrowed at 3% interest, payable in 120 days, using financial formulas. This step-by-step guide walks through the time value of money and the application of the Banker's Rule, making it ideal for high school students in Grades 10-12.

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