Final answer:
To calculate the principal repayment portions of a mortgage at different stages, we utilize the amortization formula. The first monthly payment's principal is found by subtracting the interest from the total payment. For the principal portion of the 181st payment, determine the remaining loan balance after 180 payments and then find the interest for the 181st month.
Step-by-step explanation:
Calculating the Principal Repayment for a Mortgage
To answer the student's questions, we need to use the formula for an amortizing loan to find out the portion of the payment that goes toward the principal at different stages of the loan. An amortizing loan has regular payments that are used first to pay off the interest accrued for the period and then to reduce the principal balance of the loan.
First Monthly Payment Principal
The formula to calculate the monthly mortgage payment is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
- M is the total monthly mortgage payment
- P is the principal loan amount
- i is the monthly interest rate, which is the annual interest rate divided by 12
- n is the number of payments (the number of months)
For the given mortgage:
- P = $125,000
- Annual interest rate = 5.5%
- Monthly interest rate = 5.5% / 12 months = 0.0045833
- n = 30 years x 12 months/year = 360 months
The monthly payment M can be calculated using the values above.
Then, the interest portion of the first payment is calculated as:
Interest = P x i
And the principal portion is M minus this interest.
Principal of the 181st Payment
To find the principal portion of the 181st payment, after 15 years, we would need to calculate the remaining balance of the loan after 180 payments and calculate the interest on this new balance for the 181st payment. Then we subtract that interest from the monthly payment to find the principal repayment for that month.
Using a loan amortization schedule or financial calculator can help to make these calculations more efficiently.