To determine the principal balance after the first month's payment, we need to find the initial loan amount and the interest rate.
The initial loan amount is the purchase price of the mobile home minus the down payment and the sales tax.
Initial loan amount = $89,000 - $3,000 - (4.2% * $89,000) = $81,738
Next, we need to determine the interest rate based on your parents' credit score. Since the problem states that they have an "average" credit score, we will use the average interest rates for secured and unsecured credit with an APR of 5.85% and 6.75%, respectively. Since this is a mobile home purchase, we will assume that the loan is secured and use an interest rate of 5.85%.
Using these values, we can calculate the principal balance after the first month's payment using the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, C is the monthly payment, r is the monthly interest rate (5.85% / 12 = 0.4875%), and n is the number of months (30 years or 360 months).
Substituting the given values, we get:
PV = $925.67 * [(1 - (1 + 0.004875)^(-360)) / 0.004875]
PV = $81,276.05
Therefore, the principal balance after applying the first month's payment is $81,276.05.
Answer: B. $88,245.05 is not correct, the correct answer is $81,276.05