You have recently taken a loan out in the amount of \( \$ 210,000 \) for a new home. You place \( 10 \% \) down and finance the remaining balance. As part of the closing cost, you are required to pay 4 points. Determine the amount of the loan prior to the addition of 4 points to the loan. Round your answer to the nearest cent. \( \begin{array}{ll}\text { a. } \$ 201,923.08 & \text { c. } \$ 207,980.77 \\ \text { b. } \$ 203,942.31 & \text { d. } \$ 205,961.54\end{array} \)

To determine the amount of the loan prior to the addition of 4 points, we first need to calculate the down payment and the financed amount. 1. **Calculate the down payment:** The down payment is \( 10\% \) of the home price. \[ \text{Down payment} = 0.10 \times 210,000 = 21,000 \] 2. **Calculate the financed amount:** The financed amount is the total price minus the down payment. \[ \text{Financed amount} = 210,000 - 21,000 = 189,000 \] 3. **Calculate the points:** Points are calculated as a percentage of the loan amount. In this case, 4 points means \( 4\% \) of the financed amount. \[ \text{Points} = 0.04 \times 189,000 = 7,560 \] 4. **Calculate the total loan amount including points:** The total loan amount after adding the points is: \[ \text{Total loan amount} = 189,000 + 7,560 = 196,560 \] However, the question asks for the amount of the loan prior to the addition of 4 points. The amount of the loan prior to the addition of points is simply the financed amount, which is \( 189,000 \). Since the options provided do not include \( 189,000 \), it seems there may be a misunderstanding in the interpretation of the question. The loan amount prior to points is indeed \( 189,000 \), but if we are looking for the amount that reflects the loan amount before points are added, we can check the options again. If we consider the loan amount before points are added, we can also check if the points are calculated based on the loan amount after the down payment. However, since the question specifically asks for the amount of the loan prior to the addition of points, the answer is: \[ \text{Loan amount prior to points} = 189,000 \] None of the options provided match this amount. Please verify the question or the options given.