1. **State the problem:** You want to find the maximum price you can pay for a second-hand machine if you can afford to pay 2000 per month for up to 5 years, with an interest rate of 18% per year. 2. **Formula used:** This is a present value of an annuity problem. The formula for the present value $P$ of an annuity paying $R$ per period for $n$ periods at interest rate $i$ per period is: $$P = R \times \frac{1 - (1 + i)^{-n}}{i}$$ 3. **Convert given data:** - Monthly payment $R = 2000$ - Annual interest rate = 18%, so monthly interest rate $i = \frac{18\%}{12} = 0.015$ - Number of months $n = 5 \times 12 = 60$ 4. **Calculate present value:** $$P = 2000 \times \frac{1 - (1 + 0.015)^{-60}}{0.015}$$ Calculate $(1 + 0.015)^{-60}$: $$1.015^{-60} = \frac{1}{1.015^{60}}$$ Calculate $1.015^{60}$: Using approximation or calculator, $1.015^{60} \approx 2.4596$ So, $$1.015^{-60} = \frac{1}{2.4596} \approx 0.4065$$ Now substitute back: $$P = 2000 \times \frac{1 - 0.4065}{0.015} = 2000 \times \frac{0.5935}{0.015}$$ Simplify fraction: $$\frac{0.5935}{0.015} = 39.5667$$ So, $$P = 2000 \times 39.5667 = 79,133.33$$ 5. **Round to nearest 100:** $79,133.33 \approx 79,100$ **Final answer:** You can afford to pay approximately 79,100 for the machine.