Question

Suppose you are going to purchase a house.

You negotiate a great deal and your bank agrees to lend you money for 30 years at 4% APR (annual percentage rate). HINT: For the monthly interest rate do 4/12 (4% divided by 12 months) and answer to 6 decimal places. Enter the answer in dollar format without $ sign or thousands comma -> 3519.23 and not $3,519.23 or 3,519.23 The house costs $300,000 and you pay 20% down and finance the rest. Compute (round it to 2 numbers after the decimal point for the answer inputs but not for interim steps)
(1) Monthly payment:
(2) The interest payment portion of 1st Monthly payment:
(3) The principal payment portion of the 1st Monthly payment:
(4) Balance after the 1st payment:

Answer 1

(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

Step-by-step 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