1. **State the problem:** You want to find the maximum price you can afford for a second-hand machine if you can pay N2000 per month for up to 5 years, with an interest rate of 18% per year. 2. **Identify the formula:** 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 the present value:** $$P = 2000 \times \frac{1 - (1 + 0.015)^{-60}}{0.015}$$ 5. **Calculate $(1 + 0.015)^{-60}$:** $$ (1.015)^{-60} = \frac{1}{(1.015)^{60}} $$ Calculate $(1.015)^{60}$: $$ (1.015)^{60} \approx 2.4596 $$ So: $$ (1.015)^{-60} \approx \frac{1}{2.4596} = 0.4065 $$ 6. **Substitute back:** $$P = 2000 \times \frac{1 - 0.4065}{0.015} = 2000 \times \frac{0.5935}{0.015}$$ 7. **Simplify fraction:** $$ \frac{0.5935}{0.015} = 39.5667 $$ 8. **Calculate $P$:** $$P = 2000 \times 39.5667 = 79,133.33$$ 9. **Round to nearest 100:** $$P \approx 79,100$$ **Final answer:** You can afford to pay approximately N79,100 for the machine.