1. **Stating the problem:** You have two payment options for a phone: - Cash price: 13,499 - Installment: 2,500 per month for 6 months at 9% interest compounded monthly. You must decide whether it's better to pay cash now or pay in installments. 2. **Calculating the total cost if paid in installments:** The interest rate per month is $\frac{9}{12} = 0.75\% = 0.0075$. We treat this as a loan with 6 payments of 2,500 each, monthly. The present value $PV$ of the installment payments is: $$ PV = P \times \frac{1 - (1+r)^{-n}}{r} $$ where $P=2500$, $r=0.0075$, and $n=6$. Calculate: $$ PV = 2500 \times \frac{1 - (1+0.0075)^{-6}}{0.0075} $$ First find $(1+0.0075)^{-6} = (1.0075)^{-6}$. Compute $1.0075^6 \approx 1.046$, so inverse is $\frac{1}{1.046} \approx 0.956$. Then: $$ PV = 2500 \times \frac{1 - 0.956}{0.0075} = 2500 \times \frac{0.044}{0.0075} = 2500 \times 5.867 = 14,667.50 $$ 3. **Comparing the costs:** - Cash price = 13,499 - Present value of installments = 14,667.50 Installments cost more by $14,667.50 - 13,499 = 1,168.50$. 4. **Answering the questions:** - If I were the buyer, I prefer to pay cash because it costs less overall. - Cash payment avoids interest charges embedded in the installment plan. - The advantage of paying cash is you pay less money in total and own the phone immediately. - The advantage of installments is spreading payments over time, which helps manage cash flow. 5. **Summary:** Choosing cash saves around 1,169 compared to installments under the given interest rate, but installments offer the flexibility of payments over six months. Thus, the choice depends on your financial situation and preference for upfront cost versus monthly affordability.