The problem presented is comparing two loan options:

1. Option 1: A 30-year loan with an APR of 9.5%, where the monthly payment is $1,345.40.
2. Option 2: A 15-year loan with an APR of 8.5%, where the monthly payment is $1,575.60.

To make the comparison meaningful, we will compute:

1. Total payments for each loan (monthly payment × total number of months).
2. Interest paid for each loan (total payments - principal, which is $160,000).

Let's calculate:

Total payments for Option 1:

• Loan term: 30 years = 30 × 12 = 360 months.
• Total payment = $1,345.40 × 360 = $484,344.

Total payments for Option 2:

• Loan term: 15 years = 15 × 12 = 180 months.
• Total payment = $1,575.60 × 180 = $283,608.

Interest paid for Option 1:

• Interest = Total payment - Loan amount = $484,344 - $160,000 = $324,344.

Interest paid for Option 2:

• Interest = Total payment - Loan amount = $283,608 - $160,000 = $123,608.

Summary:

• Option 1 (30 years): Total payment = $484,344, Interest paid = $324,344.
• Option 2 (15 years): Total payment = $283,608, Interest paid = $123,608.

Would you like to see more details or calculations?

Here are 5 follow-up questions:

1. How is the total payment affected by the interest rate and loan term?
2. Why does the 15-year loan have less interest compared to the 30-year loan?
3. What is the benefit of a lower APR in the long run?
4. How does a higher monthly payment reduce the overall interest paid?
5. What role does loan term play in determining total cost?

Tip: When considering loans, a shorter loan term often means higher monthly payments but significantly less interest paid over time.