Question: Use \[ \frac{P}{1 - (1 + r)^{-n}} \] to determine the regular payment amount, rounded to the…

Use \[ \frac{P}{1 - (1 + r)^{-n}} \] to determine the regular payment amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a $190,000 mortgage. Which mortgage loan has the larger total cost (closing costs + the amount paid for points + total cost of interest)? By how much? Mortgage A: 30-year fixed at 12.25% with closing costs of $1500 and 3 points. Mortgage B: 30-year fixed at 11.25% with closing costs of $1500 and 4 points. Choose the correct answer below, and fill in the answer box to complete your choice. (Do not round until the final answer. Then round to the nearest dollar as needed.) A. Mortgage B has a larger total cost than mortgage A by $ B. Mortgage A has a larger total cost than mortgage B by $

Solution

To compare the total loan costs of the two mortgage options, we need to calculate the total cost for each option, which includes the closing costs and the present value of the points and interest paid over the loan term. Given: - Mortgage A: 30-year fixed at 10.25% with $1500 closing costs and 1 point. - Mortgage B: 30-year fixed at 11.25% with $1500 closing costs and 0 points. The cost of a point is typically 1% of the loan amount, but let’s calculate more precise total costs step by step. Step 1: Calculate the cost of the point for Mortgage A The loan amount is $190,000. Cost of 1 point = 1% of $190,000 = $1,900. Step 2: Calculate the total of closing costs and points For Mortgage A: \[ \text{Total costs} = 1500 + 1900 = 3400 \] For Mortgage B: \[ \text{Total costs} = 1500 \] Step 3: Compare the costs Difference = Total costs for Mortgage A - Total costs for Mortgage B \[ 3400 - 1500 = 1900 \] Conclusion Mortgage A has a larger total cost than Mortgage B by $1900. So, the correct answer is: B. Mortgage A has a larger total cost than Mortgage B by $1900.