uestion 7 (ro Marks) Where appropriate, give your answer correct to the nearest
ID: 1171448 • Letter: U
Question
uestion 7 (ro Marks) Where appropriate, give your answer correct to the nearest cent. Jack borrows $550,000 on a 30-year home loan to purchase an apartment. The bank charges an interest rate of 6% p a compounded monthly and Jack agrees to make monthly repayments at the end of each month. a) Show a formula calculation (and workingshto confirm the monthly repayment is approximately $3,297.53. (3 marks) b) Complete the loan amortisation schedule for the last month (i.e. 360th month) of the loan. (Assume that the interest rate remains the same). (3 marks) Month Loan Balance (beginning of Interest 360 Workings: Repayment Loan Balance end of month) c) Calculate the total amount of interest paid over the thirty years (4 marks)Explanation / Answer
Requirement – a, Calculation of Monthly Repayment
Monthly Interest Rate = 6%/12 = 0.50%
Number of Period = 30 Years x 12 Months = 360 Periods
Monthly Payment = [ P x { r ( 1+r)n } ] / ( 1+r)n – 1
= [ $550,000 x { 0.005 x ( 1.005)360 } ] / ( 1.005)360 – 1
= [ $550,000 x { 0.005 x 6.022575 } ] / 5.022575
= [ $550,000 x 0.030113 ] / 5.022575
= $3,297.53 / Month
Requirement – b, Amortization schedule for the last month
Month
Loan Balance (Beginning Month)
Interest
Repayment
Loan Balance (End of month)
360
3278.79
16.39
3278.79
0
Requirement – C, Total Amount of Interest Paid over 30 Years
Total Interest Paid = Total Payment - Mortgage Loan Amount
= [$3297.53 x 360 Month ] - $550,000
= $ 1,187,110.80 - 550,000
= $ 637,110.80
Month
Loan Balance (Beginning Month)
Interest
Repayment
Loan Balance (End of month)
360
3278.79
16.39
3278.79
0
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