Question

You are planning on purchasing a $1,000,000 home with a 20% down payment. Assume 30 years for the mortgage. The bank quotes you a 6% interest rate (APR).

(i) Calculate the monthly payment

(ii) Calculate the EAR on the loan

(iii) Amortize the first 2 payments

Answer 1

Answer a.

Cost of home = $1,000,000

Down payment = 20% * $1,000,000
Down payment = $200,000

Amount borrowed = $1,000,000 - $200,000
Amount borrowed = $800,000

Time period = 30 years or 360 months

Annual interest rate = 6.00%
Monthly interest rate = 0.50%

Let monthly payment be $x

$800,000 = $x/1.005 + $x/1.005^2 + … + $x/1.005^359 + $x/1.005^360
$800,000 = $x * (1 - (1/1.005)^360) / 0.005
$800,000 = $x * 166.791614
$x = $4,796.40

Monthly payment = $4,796.40

Answer b.

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.005)^12 - 1
Effective annual rate = 1.0617 - 1
Effective annual rate = 0.0617 or 6.17%

Answer c.

Period Beginning Loan Outstanding $ 800,000.00 $ $ 799,203.60 $ Repayment of Ending Loan Cash Paid Interest Paid Principal Outstanding 4,796.40 $ 4,000.00 $ 796.40 $ 799,203.60 4,796.40 $ 3,996.02 $ 800.38 $ 798,403.22