You have just applied, and have been approved for a $250,000 mortgage. The rate quoted to you by the lender is 5.0% for a 30 year fixed mortgage. Use the table provided to determine how much of your first month's payment goes towards the principal.
Monthly Payments per $1000 of Mortgage
| Interest Rate (%) | 10 Years | 20 Years | 30 Years | 40 Years |
| :----------------- | :------- | :------- | :------- | :------- |
| 5.0 | 10.61 | 6.60 | 5.37 | 4.83 |
| 5.5 | 10.86 | 6.88 | 5.68 | 5.16 |
| 6.0 | 11.11 | 7.17 | 6.00 | 5.51 |
| 6.5 | 11.36 | 7.46 | 6.33 | 5.86 |
A. $359.21
B. $393.21
C. $339.21
D. $300.83
Answer (2)
Find the monthly payment per $1000 from the table: $5.37.
Calculate the total monthly payment: $5.37 \times 250 = $1342.50.
Calculate the monthly interest payment: $250000 \times (0.05 / 12) = $1041.67.
Calculate the principal payment: $1342.50 - $1041.67 = \boxed{$300.83}.
Explanation
Understanding the Problem We are given a mortgage of $250,000 with an interest rate of 5.0% for a 30-year term. We need to determine how much of the first month's payment goes towards the principal. The table provides monthly payments per $1000 of mortgage.
Finding Monthly Payment per $1000 First, we need to find the monthly payment per $1000 of mortgage from the table for a 5.0% interest rate and a 30-year term. From the table, this value is $5.37.
Calculating Total Monthly Payment Next, we calculate the total monthly payment by multiplying the monthly payment per $1000 by the total mortgage amount in thousands: Total monthly payment = 5.37 × 1000 250000 = 5.37 × 250 = $1342.50
Calculating Monthly Interest Payment Now, we calculate the monthly interest payment using the formula: Monthly interest payment = Mortgage amount × 12 Interest rate = 250000 × 12 0.05 = $1041.67 (rounded to the nearest cent).
Calculating Principal Payment Finally, we calculate the amount of the first month's payment that goes towards the principal by subtracting the monthly interest payment from the total monthly payment: Principal payment = Total monthly payment − Monthly interest payment = 1342.50 − 1041.67 = $300.83
Final Answer Therefore, the amount of the first month's payment that goes towards the principal is $300.83 .
Examples
Understanding mortgage calculations is crucial for financial planning. For instance, if you're buying a house, knowing how much of your monthly payment goes towards the principal helps you estimate how quickly you'll build equity. This knowledge can inform decisions about refinancing or making extra payments to shorten the loan term and save on interest. It's also useful for comparing different mortgage offers and understanding the long-term costs of homeownership.
The amount of the first month's payment that goes towards the principal is approximately $300.83. This is calculated by determining the total monthly payment and subtracting the interest payment. Therefore, the correct answer is D. $300.83.
;
