Keith bought a lakeside cottage for 30% down and monthly mortgage payments of $1224.51 at the end of each month for 20 years. Interest is 4.4% compounded monthly. What is the purchase price of the property?

Question

Quizplus · Accepted Answer

First, we need to determine the total number of payments made over the 20-year mortgage period. There are 12 months in a year, so there will be a total of 20 x 12 = 240 payments made.

Next, we can use the mortgage formula to solve for the principal value of the loan (i.e. the purchase price of the property). The formula is:

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

where:
P = principal value of the loan (i.e. purchase price of the property)
A = monthly mortgage payment
r = monthly interest rate (0.044 / 12)
n = total number of payments (240)

Plugging in the values, we get:

P = (1224.51 / ((1 - (1 + (0.044 / 12))^(-240))) / (0.044 / 12))
P = $278,878.40

Therefore, the purchase price of the property was $278,878.40. The answer is C.

Keith Bought a Lakeside Cottage for 30% Down and Monthly