Questions: Compare the monthly payment and total payment for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a 170,000 loan. Option 1: a 30-year loan at an APR of 8%. Option 2: a 15-year loan at an APR of 7%. Find the total payment for each option. The total payment for option 1 is 449064.00. The total payment for option 2 is 275041.80. (Round to the nearest cent as needed.) Compare the two options. Which appears to be the better option? A. Option 2 is the better option, but only if the borrower can afford the higher monthly payments over the entire term of the loan. B. Option 1 will always be the better option. C. Option 1 is the better option, but only if the borrower plans to stay in the same home for the entire term of the loan. D. Option 2 will always be the better option.

Solution Steps

To compare the two loan options, we need to calculate the monthly payment for each loan using the loan amount, interest rate, and loan term. The formula for the monthly payment of a fixed-rate loan is given by the annuity formula. Once we have the monthly payments, we can compare the total payments over the life of each loan. Finally, we can determine which option is better based on the total payment and the borrower's ability to afford the monthly payments.

To find the monthly payment for each loan option, we use the annuity formula for fixed-rate loans:

\[ M = \frac{P \cdot r}{1 - (1 + r)^{-n}} \]

where:

• \( M \) is the monthly payment,
• \( P \) is the principal loan amount,
• \( r \) is the monthly interest rate,
• \( n \) is the total number of payments.

For Option 1:

• \( P = 170,000 \)
• Annual interest rate = \( 0.08 \), so monthly interest rate \( r = \frac{0.08}{12} \)
• Loan term = 30 years, so \( n = 30 \times 12 = 360 \)

\[ M_1 = \frac{170,000 \times \frac{0.08}{12}}{1 - \left(1 + \frac{0.08}{12}\right)^{-360}} \approx 1247.40 \]

For Option 2:

• \( P = 170,000 \)
• Annual interest rate = \( 0.07 \), so monthly interest rate \( r = \frac{0.07}{12} \)
• Loan term = 15 years, so \( n = 15 \times 12 = 180 \)

\[ M_2 = \frac{170,000 \times \frac{0.07}{12}}{1 - \left(1 + \frac{0.07}{12}\right)^{-180}} \approx 1528.01 \]

The total payment for each loan option is calculated by multiplying the monthly payment by the total number of payments:

For Option 1: \[ \text{Total Payment}_1 = M_1 \times 360 \approx 449,063.92 \]

For Option 2: \[ \text{Total Payment}_2 = M_2 \times 180 \approx 275,041.45 \]

Comparing the total payments, we find:

• Total Payment for Option 1: \( 449,063.92 \)
• Total Payment for Option 2: \( 275,041.45 \)

Option 2 has a lower total payment, but it also has a higher monthly payment. Therefore, Option 2 is the better option if the borrower can afford the higher monthly payments over the entire term of the loan.

Final Answer