Final answer:
To find the amount of the first monthly payment that goes to repay the principal, use the formula for calculating the monthly payment of a mortgage. Subtract the interest portion from the monthly payment to find the principal portion. For this specific mortgage, the amount of the first monthly payment that goes to repay the principal is $1,662.35.
Step-by-step explanation:
To find the amount of the first monthly payment that goes to repay the principal, we need to use the formula for calculating the monthly payment of a mortgage:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount of the loan ($175,000)
r = Monthly interest rate (5.1% / 12)
n = Total number of monthly payments (30 * 12)
Once we have the monthly payment, we can calculate the principal portion of that payment by subtracting the interest portion. The interest portion can be calculated by multiplying the monthly interest rate by the remaining loan balance before the payment is made.
Let's calculate the values and find the amount of the first monthly payment that goes to repay the principal:
Monthly Payment = $1,928.72
Principal Portion = Monthly Payment - (Loan Balance * Monthly Interest Rate)
For the first monthly payment:
Loan Balance = Principal amount of the loan ($175,000)
Principal Portion = $1,928.72 - ($175,000 * 5.1% / 12)
Principal Portion = $1,662.35