Question

Please show your work as a calculation for all steps. Thank you

You have set your sights on a house in an up and coming Sydney suburb that is selling for $650,000. You are very excited about the prospects of buying this house and negotiate a 25-year mortgage with 20% down and 5.2% p.a. interest rate, compounded monthly.

B1. What will be the amount of your monthly payments?

B2. For each month for the duration of your mortgage calculate how much of your monthly payment goes to principal re-payment and how much of it is interest. Plot a graph showing a breakdown of your periodic payment into principal repayment and interest. What percentage of your monthly payment on the 36^th month of the mortgage contract goes towards repayment of the principal?

B3. After how long will the principal outstanding be reduced by a half (i.e., equal to half of the initial loan amount)?

B4. What is the amount of total interest you will end up paying over the life of the mortgage?

Answer 1

Part B1:

Total Cost = 650,000

Down payment = 20% x 650000 = 130000

Loan amount = Total cost - Down payment = 650000-130000 = 520000

Now to calculate the monthly payments, we need to solve the following equation:

Part B2:

• Opening balance = previous year's closing balance
• Closing balance = Opening balance +loan -principal repayment
• Interest = 0.052/12 x opening balance
• Principal = PMT - Interest

According to the below table: In 36th month interest = 2114.87 and principal repayment = 985.90 total PMT = 3100.77 So 985.90/3100.77 x 100 = 31.80%

Part B3:

reproducing a portion of the above schedule:

Month	Opening balance	Loan	PMT	Interest	Principal	Closing balance
195	263089.3065		3100.767896	1140.053661	1960.714235	261128.5922
196	261128.5922		3100.767896	1131.557233	1969.210663	259159.3816

half of the loan amount = 520000/2 = 260000

We see that in between the 195th and the 196th months, the loan amount is reduced to half, so the approx answer should be 196th month or 16.33 years

Part B4: Total amount of interest can be achieved using the sum of the interest column in the above table which is = $410,230.37