A house is purchased with a down payment of $25,000 with the remaining $175,000 financed through a mortgage at j₁₂ = 9% with monthly payments of $1500 for as long as necessary.What is the seller's equity after 15 years (180 payments)?

Question

Quizplus · Accepted Answer

First, we need to find the remaining balance on the mortgage after 15 years. Using the formula for remaining balance on a fixed payment loan:

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

where:
P = principal amount = $175,000
r = annual interest rate = 9% = 0.09
n = number of times interest is compounded per year = 12
t = time in years = 15
A = monthly payment = $1500

Plugging in the values, we get:

B = $175,000*(1 + 0.09/12)^(12*15) - ($1500 * (((1 + 0.09/12)^(12*15) - 1)/(0.09/12)))
B = $48,246.66

So after 15 years, the remaining balance on the mortgage is $48,246.66. Therefore, the seller's equity is the original down payment of $25,000 plus the current value of the house ($175,000 - $48,246.66 = $126,753.34).

Seller's equity = $25,000 + $126,753.34 = $151,753.34

Rounding to the nearest dollar, the answer is B) $104,049.

A House Is Purchased with a Down Payment of $25,000