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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.

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Answer to a math question 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.

Expert avatar
Sigrid
4.5
115 Answers
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

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