A $100,000, 30 year fixed rate mortgage at 8% interest has monthly principal and interest payments of $733.76. What is the loan balance after the first payment?
1st Month:I = Po*r*t
r = (8%/12) / 100% = 0.0066666 = Monthly
% rate expressed as a decimal.
t = 1 month.
I = 100000*0.0066666*1 = $666.67.
P = 733.76 - 666.67 = $67.09 = Amt applied to Po.
Bal. = 100000 - 67.09 = $99,932.91.
To calculate the loan balance after the first payment, you need to consider the loan's original balance, the interest rate, and the term. Here's how you can calculate it step by step:
1. Determine the monthly interest rate: Start by dividing the annual interest rate by 12. In this case, 8% divided by 12 equals 0.67% (0.08/12 = 0.0067).
2. Calculate the monthly interest payment: Multiply the loan balance by the monthly interest rate. For the first payment, the loan balance is the original loan amount, which is $100,000. So, the interest payment is $100,000 multiplied by 0.0067, resulting in $670 ($100,000 * 0.0067 = $670).
3. Calculate the monthly principal payment: Subtract the interest payment from the total monthly payment. In this case, $733.76 - $670 equals $63.76 ($733.76 - $670 = $63.76). This amount represents the monthly reduction in the loan balance.
4. Calculate the new loan balance: Subtract the principal payment from the original loan balance. The new loan balance is $100,000 - $63.76, which equals $99,936.24 ($100,000 - $63.76 = $99,936.24).
Therefore, after the first payment, the loan balance would be $99,936.24.