Final answer:
To answer the student's question, calculation of the monthly payment using the amortization formula is required, followed by separating the interest from the principal for each requested time period. This involves using financial mathematics principles and can be aided by an amortization calculator to precisely determine the breakdown of payments and remaining balance at certain intervals.
Step-by-step explanation:
The question you're asking involves calculating the payments and interest on a loan, which is a mathematical exercise using the principles of finance mathematics specifically dealing with amortization schedules.
Calculating the Initial Payments
To calculate the principal and interest paid in the first month of a $300,000 loan at a 4.9% APR over 30 years with monthly payments, we would start by calculating the monthly payment using the amortization formula. Then, using the monthly payment, we would calculate how much of that is interest by multiplying the total loan amount by the monthly interest rate (APR/12). The rest of the monthly payment goes towards the principal. The exact calculations for principal and interest in the first month and first year require the monthly payment amount to be known first, which can be computed using an amortization calculator or financial function in a spreadsheet.
For question (c), the interest paid in year 8 would be the sum of interest portions from each month's payment during that year, calculated from the outstanding balance at the start of year 8. Finally, the loan's remaining balance after 15 years would be calculated by determining what portion of each payment has reduced the principal over those 15 years.