Final answer:
The initial mortgage is $100,000 and the monthly mortgage payment is $449.04. The interest and principal for the first month are $291.67 and $157.37 respectively.
Step-by-step explanation:
To calculate the initial mortgage, we need to subtract the down payment from the purchase price. The down payment is 20% of $125,000, so it is $25,000. Therefore, the initial mortgage is $125,000 - $25,000 = $100,000.
To calculate the monthly mortgage payment, we can use the formula for a fixed-rate mortgage:
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where P is the initial mortgage ($100,000), r is the monthly interest rate (3.5% / 12), and n is the total number of payments (30 years * 12 months per year).
By plugging in the values and simplifying the equation, we find that the monthly mortgage payment is $449.04.
To calculate the interest and principal for the first month, we can use an amortization schedule. In the first month, the interest portion of the payment is the initial mortgage amount multiplied by the monthly interest rate (0.035 / 12) = $291.67. The principal portion is the monthly payment minus the interest portion = $449.04 - $291.67 = $157.37.
The remaining balance after 20 years can be calculated by subtracting the number of payments made (20 years * 12 months per year) from the total number of payments (30 years * 12 months per year), and then using the same formula as before with the remaining number of payments. By plugging in the values, we find that the remaining balance after 20 years is $72,828.13.
The remaining balance will be $50,000 after closely 225 months.