You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.

10% off deal Monthly payment: $$A=\frac{18000(1+\frac{0.09}{12})^{48}(\frac{0.09}{12})}{(1+\frac{0.09}{12})^{48}-1}=447.93$$ Total payment: $$447.93\times48=21500.64$$ No discount Monthly payment: $$A=\frac{20000(1+\frac{0.03}{12})^{48}(\frac{0.03}{12})}{(1+\frac{0.03}{12})^{48}-1}=442.69$$ Total payment: $$442.69\times48=21249.12$$ No discount is better deal