Question

Suppose you have decided to buy a house. The mortgage is a 30-year mortgage with an interest rate of 7%, compounded monthly. You borrow a total of $250,000. Given this, by the time you pay off the loan, how much in total (interest + principal) would the house cost you?

Answer 1

Amount borrowed = $250,000

Annual interest rate = 7.00%
Monthly interest rate = 7.00% / 12
Monthly interest rate = 0.58333%

Time period = 30 years or 360 months

Let monthly payment be $x

$250,000 = $x/1.0058333 + $x/1.0058333^2 + … + $x/1.0058333^359 + $x/1.0058333^360
$250,000 = $x * (1 - (1/1.0058333)^360) / 0.0058333
$250,000 = $x * 150.308175
$x = $1,663.25

Monthly payment = $1,663.25

Total amount paid = Monthly payment * Number of monthly payments
Total amount paid = $1,663.25 * 360
Total amount paid = $598,770

Therefore, the total cost of the house is $598,770