Final answer:
To calculate the amount of the first payment applied to the principal on an $82,000 loan at a 9.25% interest rate, subtract the first month's interest ($631.88) from the monthly payment ($674.59), which equals $42.51.
Step-by-step explanation:
The student is asking about how to calculate the amount of their first payment that will be applied to the principal balance of an $82,000 loan at a 9.25% interest rate for 30 years with monthly payments.
To find out how much of the first monthly payment of $674.59 goes towards the principal, we need to calculate the interest portion first. The monthly interest rate is 9.25% per year, which is 9.25%/12 months = 0.77083% per month. On an $82,000 loan, the first month's interest would be $82,000 * 0.77083/100 = $631.88.
Therefore, the amount of the first payment that goes towards the principal is the total monthly payment minus the interest payment: $674.59 - $631.88 = $42.51. So the correct answer is D. $42.51.