Question

Exactly 18 years ago, you took out a $550,000 30-year mortgage with monthly payments and

an APR of 10% compounded monthly. You have just made your 216th payment. What is the

outstanding balance on your loan?

Answer 1

Calculation of monthly payment:

Amount borrowed = $550,000
Time period = 30 years or 360 months

Annual interest rate = 10.00%
Monthly interest rate = 10.00% / 12
Monthly interest rate = 0.8333%

Let monthly payment be $x

$550,000 = $x/1.008333 + $x/1.008333^2 + … + $x/1.008333^359 + $x/1.008333^360
$550,000 = $x * (1 - (1/1.008333)^360) / 0.008333
$550,000 = $x * 113.954658
$x = $4,826.48

Monthly payment = $4,826.48

Calculation of loan outstanding:

Time period = 12 years or 144 months

Loan outstanding = $4,826.48/1.008333 + $4,826.48/1.008333^2 + … + $4,826.48/1.008333^143 + $4,826.48/1.008333^144
Loan outstanding = $4,826.48 * (1 - (1/1.008333)^144) / 0.008333
Loan outstanding = $4,826.48 * 83.678146
Loan outstanding = $403,870.90