1. **State the problem:** Edgar wants to buy a house priced at P1,500,000 but must add P152,000 for extra costs. He has P680,000 for the down payment and will receive a monthly housing subsidy of P2,500. He can get a 20-year mortgage at 12.5% annually compounded monthly. He is willing to spend up to one third of his gross monthly salary of P30,000 on payments. 2. **Calculate total upfront payment needed:** $$\text{Total upfront} = P680,000 + P152,000 = P832,000$$ 3. **Calculate loan amount (principal) required:** $$\text{Loan} = P1,500,000 - P832,000 = P668,000$$ 4. **Calculate the maximum monthly payment Edgar can afford:** $$\text{Max monthly payment} = \frac{1}{3} \times 30,000 = P10,000$$ 5. **Calculate monthly interest rate:** $$i = \frac{12.5\%}{12} = 1.0417\% = 0.010417$$ 6. **Calculate total number of monthly payments:** $$n = 20 \times 12 = 240$$ 7. **Calculate monthly mortgage payment using formula:** $$P = \text{loan principal} = 668,000$$ $$M = P \times \frac{i(1+i)^n}{(1+i)^n - 1}$$ Calculate numerator: $$i(1+i)^n = 0.010417 \times (1.010417)^{240}$$ Approximate: $$(1.010417)^{240} \approx e^{240 \times \ln(1.010417)} \approx e^{240 \times 0.010365} = e^{2.4876} \approx 12.03$$ Thus, $$i(1+i)^n = 0.010417 \times 12.03 \approx 0.1254$$ Calculate denominator: $$(1+i)^n -1 = 12.03 -1 = 11.03$$ So, $$M = 668,000 \times \frac{0.1254}{11.03} = 668,000 \times 0.01137 = P7,596.16$$ 8. **Add monthly housing subsidy to affordability:** Since Edgar receives P2,500 subsidy, his effective affordable payment is: $$10,000 + 2,500 = P12,500$$ 9. **Decision:** Monthly mortgage payment is P7,596.16 which is less than P12,500 affordable monthly budget. So, Edgar can afford the payments under these conditions. **Final Answer:** Edgar should buy the house as the monthly mortgage payment fits within his affordable budget.