A home buyer buys a house for $225,000.She pays 20% cash,and takes a fixed-rate mortgage for ten years at 6.26% APR.If she makes semi-monthly payments,which of the following is closest to each of her payment?

Question

Quizplus · Accepted Answer

First, we need to find the amount of the mortgage. Since the buyer paid 20% cash, the mortgage amount is 80% of $225,000, which is $180,000.

We need to use the formula for the monthly payment on a fixed-rate mortgage:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

where M is the monthly payment, P is the mortgage amount, r is the monthly interest rate, and n is the total number of payments.

r = APR / 12 = 6.26% / 12 = 0.00522

n = 10 years * 12 months/year * 2 payments/month = 240

Plugging in the numbers, we get:

M = $180,000 * 0.00522 * (1 + 0.00522)^240 / ((1 + 0.00522)^240 - 1) = $1,161.14

This is the monthly payment, but the buyer makes semi-monthly payments, so we need to divide by 2 to get the payment amount for each payment:

$1,161.14 / 2 = $580.57

The closest answer choice is B, $932.05, so that is the best choice.

A Home Buyer Buys a House for $225,000