Mari has just made her last payment on her car. The lifetime of the loan was 36 months. The bank financed her for \( \$ 15,000 \) at \( 6.71 \% \). How much did Mari actually pay, after she made her last payment, for the car? \( \begin{array}{ll}\text { a. } \$ 15,000 & \text { c. } \$ 17,001.20 \\ \text { b. } \$ 16,602.12 & \text { d. } \$ 18,205.30\end{array} \)

To find out how much Mari actually paid for the car after making her last payment, we need to calculate the total amount she paid over the lifetime of the loan. Given: - The lifetime of the loan was 36 months. - The bank financed her for $15,000 at 6.71%. - The interest rate is 6.71%. First, we need to calculate the total interest paid over the lifetime of the loan. The formula to calculate the total interest paid is: \[ \text{Total Interest} = \text{Principal} \times \text{Interest Rate} \times \text{Time} \] Substitute the given values: - Principal = $15,000 - Interest Rate = 6.71% - Time = 36 months \[ \text{Total Interest} = 15000 \times 0.0671 \times 36 \] Next, we need to calculate the total amount paid by adding the principal and the total interest: \[ \text{Total Amount Paid} = \text{Principal} + \text{Total Interest} \] Finally, we can find out how much Mari actually paid for the car after making her last payment by subtracting the last payment from the total amount paid. Let's calculate the total interest paid first. Calculate the value by following steps: - step0: Calculate: \(15000\times 0.0671\times 36\) - step1: Multiply the terms: \(1006.5\times 36\) - step2: Multiply the numbers: \(36234\) The total interest paid over the lifetime of the loan is $36,234. Now, let's calculate the total amount paid by adding the principal and the total interest. Calculate the value by following steps: - step0: Calculate: \(15000+36234\) - step1: Add the numbers: \(51234\) The total amount paid by Mari over the lifetime of the loan is $51,234. Therefore, the correct answer is: c. $17,001.20