Question

Your parents are buying a house for $187,500. they have a good credit rating or making a 20% down payment and expect to pay $1575/month. the interest rate for the mortgage is 4.65%. how muxh interest is paid at the end of the second mopnth?

Answer 1

To calculate the interest paid at the end of the second month on a mortgage, determine the loan amount after a 20% down payment, find the monthly interest rate, then calculate the interest and principal from the first payment. The interest for the second month is the remaining balance after the first month multiplied by the monthly interest rate, which for this example is $577.19.

Step-by-step explanation:

To calculate the interest paid at the end of the second month for a mortgage on a house with a sale price of $187,500, we first need to determine the loan amount by calculating the down payment. With a 20% down payment, the loan amount will be 80% of the purchase price:

• Down Payment = 20% of $187,500 = $37,500
• Loan Amount = Purchase Price - Down Payment = $187,500 - $37,500 = $150,000

Since the interest rate for this mortgage is 4.65%, and interest is typically calculated monthly on the remaining balance for such loans, we apply the monthly interest rate to the outstanding balance to find the interest for the second month. The monthly interest rate is 4.65% divided by 12.

Interest for Month 2 = Remaining Balance × Monthly Interest Rate

But first, we need to find out how much of the first payment went towards the interest and the principal to determine the remaining balance for the second month. Assuming the loan is amortized, part of the monthly payment of $1575 goes to interest and the rest to lowering the principal. We calculate the first month's interest:

• Interest for Month 1 = Loan Amount × Monthly Interest Rate
• Monthly Interest Rate = 4.65% / 12 months = 0.003875
• Interest for Month 1 = $150,000 × 0.003875 = $581.25

The principal paid in the first month is the remainder of the monthly payment after the interest:

• Principal Reduction in Month 1 = Monthly Payment - Interest for Month 1 = $1575 - $581.25 = $993.75

Hence, the remaining balance after the first month is:

• Remaining Balance after Month 1 = Loan Amount - Principal Reduction in Month 1 = $150,000 - $993.75 = $149,006.25

To find out the interest for the second month, we apply the monthly interest rate to the new balance:

• Interest for Month 2 = Remaining Balance after Month 1 × Monthly Interest Rate = $149,006.25 × 0.003875 = $577.19

The interest paid at the end of the second month would be $577.19.