Tetsuo has decided to purchase a new car. He decides to put \( 10 \% \) down and finance the remaining balance. The bank offers Tetsuo a 36 month loan at \( 6.71 \% \). If the car is valued at \( \$ 32,000 \), what will his monthly payments be? \( \begin{array}{ll}\text { a. } \$ 983.93 & \text { c. } \$ 782.65 \\ \text { b. } \$ 885.45 & \text { d. } \$ 688.88\end{array} \)

To find Tetsuo's monthly payments, we need to calculate the loan amount he will finance and then use the loan amount to determine the monthly payments. Given: - Tetsuo decides to put \(10\%\) down on the car. - The car is valued at \$32,000. - The bank offers a 36-month loan at \(6.71\%\). Let's calculate the loan amount first: Loan amount = Car value - Down payment Loan amount = \$32,000 - \(10\%\times \$32,000\) Next, we will calculate the monthly payments using the loan amount and the interest rate. Calculate the value by following steps: - step0: Calculate: \(32000-0.1\times 32000\) - step1: Multiply the numbers: \(32000-3200\) - step2: Subtract the numbers: \(28800\) The loan amount Tetsuo will finance is \$28,800. Now, let's calculate the monthly payments using the loan amount and the interest rate. Calculate the value by following steps: - step0: Calculate: \(\frac{28800}{36}\) - step1: Divide the terms: \(800\) The monthly payments for Tetsuo's car loan will be \$800. Therefore, the correct answer is: b. \$885.45