Question

Eowyn wants to buy a house that is priced at $235,000. She makes a down payment of 20% and then finances the balance with a loan that will require her to make monthly payments for thirty years, with the first payment due one month after the purchase of the house. If her lender charges 4.25% per year compounded monthly, find the outstanding loan balance after she makes 7 years of payments.

Answer 1

PV = Mortgage amount = $235,000 - (20% * $235,000) = $235,000 - $47,000 = $188,000

n = 30 *12 = 360 months

r = Monthly interest rate = 4.25%/12 = 0.35416667%

x = payments made = 7*12 = 84 months

Monthly payment = [r * PV] / [1 - (1+r)^-n]

= [0.35416667% * $188,000] / [1 - (1+0.35416667%)^-360]

= $665.83333333 / 0.71993924

= $924.846568

P = Monthly payment = $924.85

Outstanding balance after 7 years = P * [1 - (1+r)^-(n-x)] / r

= $924.85 * [1 - (1+0.35416667%)^-(360-84)] / 0.35416667%

= $924.85 * 0.623099482 / 0.0035416667

= $162,712.532

Therefore, Outstanding balance after 7 years is $162,712.53