A vacation home has a mortgage of $120,000 for 15 years at an annual interest rate of 6%. a. Find the monthly mortgage payment.
b. During a month when $384.8 of the monthly mortgage payment is principal, how much of the payment is interest?

Question

Quizplus · Accepted Answer

a. We can use the formula for the monthly payment of a mortgage given by:

P = (r(PV))/(1-(1+r)^(-n))

where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (in this case, $120,000), and n is the total number of payments (in this case, 15 years or 180 months).

First, we need to find the monthly interest rate. Since the annual rate is 6%, the monthly rate is 6%/12 = 0.005.

Plugging this into the formula, we get:

P = (0.005(120000))/(1-(1+0.005)^(-180)) = $1012.63

So the monthly mortgage payment is $1012.63.

b. We know that the total monthly payment is $1012.63, and $384.8 of that is going toward principal. To find how much is going toward interest, we can subtract the principal payment from the total payment:

Interest payment = Total payment - Principal payment
Interest payment = $1012.63 - $384.8
Interest payment = $627.83

So during a month when $384.8 of the monthly mortgage payment is principal, $627.83 of the payment is interest.

A Vacation Home Has a Mortgage of $120,000 for 15