1. **State the problem:** A person can either pay P6,500,000 cash now or pay P4,000,000 down and P4,200,000 after 5 years. Money earns 8% annual interest compounded quarterly. We want to determine which purchase plan is better and by how much. 2. **Calculate the present value (PV) of the deferred payment of P4,200,000 in 5 years:** The quarterly interest rate is $$\frac{8\%}{4} = 2\% = 0.02$$ per quarter. Number of quarters in 5 years: $$5 \times 4 = 20$$. Use the present value formula for a single future payment: $$PV = \frac{FV}{(1 + i)^n}$$ where $$FV = 4,200,000$$, $$i=0.02$$, $$n=20$$. Calculation: $$PV = \frac{4,200,000}{(1+0.02)^{20}} = \frac{4,200,000}{(1.02)^{20}}$$ Calculate $$ (1.02)^{20} $$: $$ (1.02)^{20} = 1.485947 $$ (approx) Therefore: $$ PV = \frac{4,200,000}{1.485947} \approx 2,825,913.85 $$ 3. **Calculate total present value of the installment plan:** $$ Total ext{ }PV = 4,000,000 + 2,825,913.85 = 6,825,913.85 $$ 4. **Compare the two options:** - Cash payment: P6,500,000 - Installment plan present value: P6,825,913.85 5. **Interpretation:** Since the present value of the installment plan is higher than the cash payment, paying cash now is cheaper. 6. **By how much is cash payment better?** $$ Difference = 6,825,913.85 - 6,500,000 = 325,913.85 $$ **Answer:** Pay cash now to save approximately P325,914 compared to the installment plan.