Question

Marcel Thiessen purchased a home for $203,400 and obtained a 15-year, fixed-rate mortgage at 7% after paying a down payment of 10%. Of the first month's mortgage payment, how much is interest and how much is applied to the principal? (Round your answer to the nearest cent.)

interest	$
applied to the principal	$

Answer 1

Total cost = $203400

Down payment = 10% * $203400 = $20340

Mortgage amount = $203400 - $20340 = $183060

Now, we will calculate the monthly payment for the motgage:

Here, the cash inflow will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity = $183060, P is the monthly amount , r is the rate of interest = 7%. Monthly rate = 7% / 12 = 0.5833% and n is the time period = 15 * 12 = 180 months

Now, putting these values in the above formula, we get,

$183060 = P * (1 - (1 + 0.58333%)-180 / 0.583333%)

$183060 = P * (1 - ( 1+ 0.005833)-180 / 0.0058333)

$183060 = P * (1 - ( 1.0058333)-180 / 0.0058333)

$183060 = P * (1 - 0.35100712332) / 0.0058333)

$183060 = P * (0.64899287668 / 0.0058333)

$183060 = P * 111.2559852914202

P = $183060 / 111.2559852914202

P = $1645.40

So, monthly payment is $1645.40

On first month's mortgage:

Interest = $183060 * 0.58333% = $1067.85

Principal = Monthly payment - Interest

Principal = $1645.4 - $1068 = $577.55