Final answer:
a) The loan amount will be $201,600. b) The monthly payments can be calculated using the formula for a fixed-rate mortgage payment. c) The interest portion of the first payment can be found by multiplying the loan amount by the monthly interest rate.
Step-by-step explanation:
a) To calculate the loan amount, we need to subtract the down payment from the purchase price of the home. The down payment is 20% of $252,000, which is $50,400. So the loan amount will be $252,000 - $50,400 = $201,600.
b) To find the monthly payments, we can use the formula for a fixed-rate mortgage payment: P * r * (1 + r)^n / ((1 + r)^n - 1), where P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments. The monthly interest rate is 5.45% divided by 12, or 0.4542%. The number of monthly payments is 30 years * 12 months per year, or 360. Plugging these values into the formula, we get: ($201,600 * 0.4542% * (1 + 0.4542%)^360) / ((1 + 0.4542%)^360 - 1). Calculating this expression gives us the monthly payment.
c) The first payment consists of both principal and interest. To calculate the interest portion of the first payment, we can multiply the loan amount by the monthly interest rate, which gives us the monthly interest. This amount will be deducted from the total monthly payment to find the principal portion.