You have decided to purchase a car for \( \$ 22,346.16 \). The credit union requires a \( 10 \% \) down payment and will finance the balance with a \( 5.4 \% \) annual interest loan for 36 months. The sales tax in your city is \( 7.6 \% \), and the license and title charges are \( \$ 125.13 \). Determine the amount that the credit union will finance you for. Round your answer to the nearest cent. \( \begin{array}{ll}\text { a. } \$ 24,179.10 & \text { c. } \$ 21,761.20 \\ \text { b. } \$ 24,169.60 & \text { d. } \$ 21,752.64\end{array} \)

To determine the amount that the credit union will finance, we need to follow these steps: 1. **Calculate the down payment**: \[ \text{Down Payment} = \text{Car Price} \times \text{Down Payment Percentage} \] \[ \text{Down Payment} = 22,346.16 \times 0.10 = 2,234.62 \] 2. **Calculate the sales tax**: \[ \text{Sales Tax} = \text{Car Price} \times \text{Sales Tax Percentage} \] \[ \text{Sales Tax} = 22,346.16 \times 0.076 = 1,696.00 \] 3. **Calculate the total cost of the car including sales tax and license/title charges**: \[ \text{Total Cost} = \text{Car Price} + \text{Sales Tax} + \text{License and Title Charges} \] \[ \text{Total Cost} = 22,346.16 + 1,696.00 + 125.13 = 24,167.29 \] 4. **Calculate the amount to be financed**: \[ \text{Amount Financed} = \text{Total Cost} - \text{Down Payment} \] \[ \text{Amount Financed} = 24,167.29 - 2,234.62 = 21,932.67 \] Now, let's check the options provided: - a. \( \$ 24,179.10 \) - b. \( \$ 24,169.60 \) - c. \( \$ 21,761.20 \) - d. \( \$ 21,752.64 \) None of the options match the calculated amount of \( 21,932.67 \). Let's double-check the calculations: 1. **Down Payment**: \[ 22,346.16 \times 0.10 = 2,234.62 \] 2. **Sales Tax**: \[ 22,346.16 \times 0.076 = 1,696.00 \] 3. **Total Cost**: \[ 22,346.16 + 1,696.00 + 125.13 = 24,167.29 \] 4. **Amount Financed**: \[ 24,167.29 - 2,234.62 = 21,932.67 \] It appears that the calculations are correct, but the options provided do not include the correct amount. If we consider the possibility of rounding or misinterpretation of the sales tax or other fees, we can check the calculations again, but based on the provided data, the amount financed is \( 21,932.67 \). Please verify the problem statement or the options provided.