Final answer:
To answer the student's question, a detailed calculation using the amortization formula is applied to produce a monthly payment value. From there we calculate the portions of interest and principal within the first three months' payments on a $141,000 home mortgage with a fixed 3% APR over 30 years, ultimately creating the requested table.
Step-by-step explanation:
To create a table showing the amount of each monthly payment that goes toward principal and interest for the first three months of a home mortgage of $141,000 with a fixed APR of 3% for 30 years we first need to calculate the monthly payment. to determine the monthly payment, we can use the formula for an amortized loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where,
M = monthly mortgage payment
P = principal loan amount
i = monthly interest rate
n = number of payments (terms in months)
The monthly interest rate is 0.03 (annual rate) divided by 12, i.e., 0.0025. The total number of payments for a 30-year mortgage is 30 * 12 (months) = 360. Plugging in these numbers, we calculate the monthly payment. Next, we need to calculate the interest and principal portions for the first three payments. In the initial months, a larger portion of payments goes toward interest than principal. As we continue to make payments, this starts to shift more towards the principal. For each of the first three months:
- Compute the interest for the month: Interest = outstanding principal * monthly interest rate.
- Subtract the interest from the total monthly payment to find the amount that goes towards the principal.
- Subtract the principal payment from the outstanding balance to find the new outstanding balance for the next month.
Using this information, we can then construct a table for the first three months.