1. **Problem statement:** A car costs 165000. The buyer makes a down payment and finances the rest with monthly payments of 5837.55 for 2 years at 15% annual interest compounded monthly. Find the down payment amount. 2. **Formula used:** The loan balance is the present value of an annuity: $$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$$ where $P$ is the monthly payment, $i$ is the monthly interest rate, and $n$ is the total number of payments. 3. **Calculate monthly interest rate:** $$i = \frac{15\%}{12} = 0.15 / 12 = 0.0125$$ 4. **Calculate total number of payments:** $$n = 2 \times 12 = 24$$ 5. **Calculate present value of the loan (amount financed):** $$PV = 5837.55 \times \frac{1 - (1 + 0.0125)^{-24}}{0.0125}$$ 6. **Calculate $(1 + 0.0125)^{-24}$:** $$1.0125^{-24} = \frac{1}{1.0125^{24}} \approx \frac{1}{1.34935} = 0.7413$$ 7. **Calculate numerator:** $$1 - 0.7413 = 0.2587$$ 8. **Calculate fraction:** $$\frac{0.2587}{0.0125} = 20.696$$ 9. **Calculate present value:** $$PV = 5837.55 \times 20.696 = 120,395.00$$ 10. **Calculate down payment:** $$\text{Down payment} = \text{Car price} - PV = 165,000 - 120,395 = 44,605$$ **Answer:** The down payment is R44605.00, which corresponds to option a.