Question

A borrower has a 30-year mortgage loan for $220,000 with an interest rate of 4.5% and monthly payments. If she wants to pay off the loan after 6 years, what would be the outstanding balance on the loan? (Show work with calculator strokes)

Answer 1

PV = Mortgage Loan = $220,000

n = 30*12 = 360 months

r = monthly interest rate = 4.5%/12 = 0.375%

n = 30*12 = 360 months

x = 6*12 = 72 months

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

= [0.375% * $220,000] / [1 - (1+0.375%)^-360]

= $825 / 0.740104346

= $1,114.70768

= $1,114.71

P = Monthly loan payment = $1,114.71

Outstanding loan balance after 6 years = P * [1 - (1+r)^-(n-x)] / r

= $1,114.71 * [1 - (1+0.375%)^-(360-72)] / 0.375%

= $1,114.71 * 0.659717815 / 0.00375

= $196,105.079

Therefore, Outstanding balance after 6 years is $196,105.08