Answer:
(1) Monthly payment: 1145.74.
(2) Interest payment portion of 1st Monthly payment: 799.92
(3) Principal payment portion of the 1st Monthly payment: 345.82
(4) Balance after the 1st payment: 239654.18
Explanation:
Note: The following instruction in the question was adhered to througout while answering this question:
Enter the answer in dollar format without $ sign or thousands comma -> 3519.23 and not $3,519.23 or 3,519.23.
(1) Monthly payment:
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or amount borrowed from bank = House cost - Down payment = 300000 - (300000 * 20%) = 240000
P = Monthly payment = ?
r = Monthly interest rate = annual percentage rate (APR) / Number of months in a year = 4% / 12 = 0.04 / 12 = 0.003333
n = number of months = Number of years of the loan * Number of months in a year = 30 * 12 = 360
Substitute the values into equation (1) and solve for P, we have:
240000 = P * ((1 - (1 / (1 + 0.003333))^360) / 0.003333)
240000 = P * 209.471358
P = 240000 / 209.471358 = 1145.74
Therefore, monthly payment is 1145.74.
(2) The interest payment portion of 1st Monthly payment:
Interest payment portion of 1st Monthly payment = PV * r = 240000 * 0.003333 = 799.92
(3) The principal payment portion of the 1st Monthly payment:
Principal payment portion of the 1st Monthly payment = P - Interest payment portion of 1st Monthly payment = 1145.74 - 799.92 = 345.82
(4) Balance after the 1st payment:
Balance after the 1st payment = PV - Principal payment portion of the 1st Monthly payment = 240000 - 345.82 = 239654.18
