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Lenders often require home buyers to pay "points." A point is 1% of the purchase price of the home. In addition, the buyer also pays closing costs at the time of purchase. If a 15-year mortgage is taken out for $155,000, which mortgage loan option, A or B, has the greater total cost (closing costs + the amount paid for points + total cost of interest)? By how much? 响 P m Assume that points and closing costs are paid separately and are not included in the mortgage. Use to [¹-(¹ + )¯] determine the regular payment amount. A: Annual interest rate 6.25%; 1 point; closing costs $1200 B: Annual interest rate 5.25%; 4 points; closing costs $1200 Choose the correct answer below, and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) OA. Mortgage B has a larger total cost than mortgage A by $ B. Mortgage A has a larger total cost than mortgage B by $

Lenders often require home buyers to pay "points." A point is 1% of the purchase price of the home. In addition, the buyer also pays closing costs at the time of purchase. If a 15-year mortgage is taken out for $155,000, which mortgage loan option, A or B, has the greater total cost (closing costs + the amount paid for points + total cost of interest)? By how much? 响 P m Assume that points and closing costs are paid separately and are not included in the mortgage. Use to [¹-(¹ + )¯] determine the regular payment amount. A: Annual interest rate 6.25%; 1 point; closing costs $1200 B: Annual interest rate 5.25%; 4 points; closing costs $1200 Choose the correct answer below, and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) OA. Mortgage B has a larger total cost than mortgage A by $ B. Mortgage A has a larger total cost than mortgage B by $

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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### Mortgage Cost Comparison **Problem Statement:** Lenders often require home buyers to pay "points." A point is 1% of the purchase price of the home. In addition, the buyer also pays closing costs at the time of purchase. If a 15-year mortgage is taken out for $155,000, which mortgage loan option, A or B, has the greater total cost (closing costs + the amount paid for points + total cost of interest)? By how much? Assume that points and closing costs are paid separately and are not included in the mortgage. Use the formula: \[ \frac{P\left(\frac{r}{m}\right)}{1-\left(1+\frac{r}{m}\right)^{-n}} \] to determine the regular payment amount. ### Mortgage Options: - **Option A:** - Annual interest rate: 6.25% - Points: 1 - Closing costs: $1200 - **Option B:** - Annual interest rate: 5.25% - Points: 4 - Closing costs: $1200 ### Question: Choose the correct answer below and fill in the answer box to complete your choice. (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 $_____. ### Explanation of the Formula: The formula given is the one for calculating the monthly payment (PMT) on an amortizing loan: \[ \text{PMT} = \frac{P \left(\frac{r}{m}\right)}{1 - \left(1 + \frac{r}{m}\right)^{-n}} \] where: - \( P \) is the principal loan amount. - \( r \) is the annual interest rate. - \( m \) is the number of payments per year. - \( n \) is the total number of payments (loan term in years times \( m \)). ### Task: Calculate the total cost of both mortgage options by: 1. Calculating the monthly payments using the given formula. 2. Summing the payments over the loan term. 3. Adding points and closing costs to find the total cost. 4. Comparing the total costs to determine which mortgage has the larger total cost and by
Transcribed Image Text:### Mortgage Cost Comparison **Problem Statement:** Lenders often require home buyers to pay "points." A point is 1% of the purchase price of the home. In addition, the buyer also pays closing costs at the time of purchase. If a 15-year mortgage is taken out for $155,000, which mortgage loan option, A or B, has the greater total cost (closing costs + the amount paid for points + total cost of interest)? By how much? Assume that points and closing costs are paid separately and are not included in the mortgage. Use the formula: \[ \frac{P\left(\frac{r}{m}\right)}{1-\left(1+\frac{r}{m}\right)^{-n}} \] to determine the regular payment amount. ### Mortgage Options: - **Option A:** - Annual interest rate: 6.25% - Points: 1 - Closing costs: $1200 - **Option B:** - Annual interest rate: 5.25% - Points: 4 - Closing costs: $1200 ### Question: Choose the correct answer below and fill in the answer box to complete your choice. (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 $_____. ### Explanation of the Formula: The formula given is the one for calculating the monthly payment (PMT) on an amortizing loan: \[ \text{PMT} = \frac{P \left(\frac{r}{m}\right)}{1 - \left(1 + \frac{r}{m}\right)^{-n}} \] where: - \( P \) is the principal loan amount. - \( r \) is the annual interest rate. - \( m \) is the number of payments per year. - \( n \) is the total number of payments (loan term in years times \( m \)). ### Task: Calculate the total cost of both mortgage options by: 1. Calculating the monthly payments using the given formula. 2. Summing the payments over the loan term. 3. Adding points and closing costs to find the total cost. 4. Comparing the total costs to determine which mortgage has the larger total cost and by
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