1. **Stating the problem:** Calculate the present value of a deferred annuity of ₱1500 every 3 months for 8 years, deferred by 3 years, with an interest rate of 6% compounded quarterly. 2. **Identify variables:** - Payment per period, $R = 1500$ - Number of payment periods, $n = 8 \times \frac{4}{1} = 32$ quarters (since 8 years and payments quarterly) - Deferral period, $t = 3$ years $= 3 \times 4 = 12$ quarters - Interest rate per period, $i = \frac{6\%}{4} = 0.015 = 1.5\%$ per quarter 3. **Calculate the present value at the start of the payout (time = 3 years):** The present value of an ordinary annuity formula is: $$PV_{start} = R \times \frac{1 - (1+i)^{-n}}{i}$$ Plugging values: $$PV_{start} = 1500 \times \frac{1 - (1.015)^{-32}}{0.015}$$ Calculate $ (1.015)^{-32} = \frac{1}{(1.015)^{32}} \approx \frac{1}{1.6047} = 0.6233$ So: $$PV_{start} = 1500 \times \frac{1 - 0.6233}{0.015} = 1500 \times \frac{0.3767}{0.015} = 1500 \times 25.112 = 37668$$ 4. **Discount back the $PV_{start}$ to present (time = 0):** The present value now is: $$PV = PV_{start} \times (1+i)^{-t} = 37668 \times (1.015)^{-12}$$ Calculate $(1.015)^{-12} = \frac{1}{(1.015)^{12}} \approx \frac{1}{1.1956} = 0.8364$ So: $$PV = 37668 \times 0.8364 \approx 31505.6$$ 5. **Match to choices given:** Closest answer is c) 31,699.67 **Final answer:** c) ₱31,699.67