Question 1193769
**1. Determine the Quarterly Interest Rate:**

* Annual Interest Rate: 8%
* Quarterly Interest Rate: 8% / 4 = 2% or 0.02

**2. Calculate the Number of Payments**

* This requires an iterative approach. We can use a spreadsheet or a financial calculator for this. 

**Here's a simplified explanation of the process:**

* **Start with an initial guess:** Let's assume 12 quarterly payments.
* **Calculate the present value of an annuity:** 
    * Use the formula: PV = PMT * [(1 - (1 + r)^-n) / r]
        * PV = Present Value (what the loan is worth today)
        * PMT = Quarterly Payment (P15,000)
        * r = Quarterly interest rate (0.02)
        * n = Number of payments (12 in this case)
* **Compare the calculated present value to the actual debt:**
    * If the calculated present value is less than the actual debt, the number of payments is insufficient. 
    * If the calculated present value is greater than the actual debt, the number of payments is excessive.
* **Adjust the number of payments accordingly and repeat the calculation.**

**Using a financial calculator or spreadsheet software (like Excel or Google Sheets) with the PV function, you'll find that it takes approximately 14 quarterly payments to pay off the debt of P175,000 with quarterly payments of P15,000 at an 8% annual interest rate.**

**Note:** This calculation assumes that the interest is compounded quarterly and that the payments are made at the end of each quarter.