Let's solve this problem using the annuities formula provided in the image. We are given the following information:

• Annual payments ($R$) = ₱1,000.00
• Term = 8 years
• Interest rate = 6% compounded quarterly
• We need to find both the Present Value (P) and Future Value (F).

Step 1: Break down the interest rate and number of periods

Since the interest is compounded quarterly, we need to adjust both the interest rate and the number of compounding periods:

• Quarterly interest rate: $j = \frac{6\%}{4} = \frac{0.06}{4} = 0.015$
• Number of periods: $n = 8 \times 4 = 32$ quarters

Step 2: Use the provided formulas

The formulas in the image are as follows:

1. Present Value (P): $P = R \times \frac{1 - (1 + j)^{-n}}{j}$
2. Future Value (F): $F = R \times \frac{(1 + j)^n - 1}{j}$

Step 3: Calculate the Present Value

Let's substitute the values into the present value formula: $P = 1,000 \times \frac{1 - (1 + 0.015)^{-32}}{0.015}$ First, calculate $1 + 0.015 = 1.015$, then raise it to the power of $-32$: $1.015^{-32} = 0.63196$ Now substitute back: