Question

6) A mortgage of $180 000 is amortized over 15 y with a 5-year term. 0 000 is amortized over 15 years at 6% compounded monthly a) Determine the monthly payment, (5 marks) Create an amortization schedule for the first 6 payments. (6 marks) Payment Monthly Interest Paid Principal Paid Outstanding Number Payment Principal 0 6 TOTAL c) How much of the 1st payment is interest? (1 mark) d) How much of the 3rd payment is used to reduce the principal? (1 mark) e) What is the total interest paid in the first 6 payments? (1 mark) What is the outstanding principal after 6 months? (1 mark)

Answer 1

Answer a.

Amount borrowed = $180,000
Annual interest rate = 6.00%
Monthly interest rate = 0.50%
Period = 15 years or 180 months

Let monthly payment be $x

$180,000 = $x/1.005 + $x/1.005^2 + … + $x/1.005^179 + $x/1.005^180
$180,000 = $x * (1 - (1/1.005)^180) / 0.005
$180,000 = $x * 118.503515
$x = $1,518.94

Monthly payment = $1,518.94

Answer b.

Payment Number 1 3 4 $ $ $ $ $ $ Monthly Outstanding Interest Paid Principal Paid Payment Principal $ 180,000.00 1,518.94 $ 900.00 $ 618.94 $ 179,381.06 1,518.94 $ 896.91 $ 622.03 $ 178,759.03 1,518.94 $ 893.80 $ 625.14 $ 178,133.89 1,518.94 $ 890.67 $ 628.27 $ 177,505.62 1,518.94 $ 887.53 $ 631.41 $ 176,874.21 1,518.94 $ 884.37 $ 634.57 $ 176,239.64 $ 5,353.28 $ 3,760.36 Total

Answer c.

Interest paid in 1st payment = $900.00

Answer d.

Principal repaid in 3rd payment = $625.14

Answer e.

Total interest paid = $5,353.28

Answer f.

Principal outstanding after 6 months = $176,239.64