Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. How much interest is paid for the second month?

Question

Be sure to include the following in your response:

the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning

Answer 1

To calculate the interest paid for the second month, you first need to determine the remaining balance after the first month's payment.

Principal amount borrowed = $187,500
Down payment (20%) = $37,500
Loan amount = $150,000 ($187,500 - $37,500)

Monthly interest rate = Annual interest rate / 12 months
Monthly interest rate = 4.65% / 12 = 0.3875%

Interest for the first month = Loan amount * Monthly interest rate
Interest for the first month = $150,000 * 0.003875 = $581.25

Principal paid in the first month = Total payment - Interest for the first month
Principal paid in the first month = $1,575 - $581.25 = $993.75

Remaining balance after the first month = Loan amount - Principal paid in the first month
Remaining balance after the first month = $150,000 - $993.75 = $149,006.25

Now, we need to calculate the interest for the second month:

Interest for the second month = Remaining balance after the first month * Monthly interest rate
Interest for the second month = $149,006.25 * 0.003875 = $578.45

Therefore, the interest paid for the second month is $578.45.