You are required to work the following problem, using compound interest techniques. You should model your answer on the text approach in Chapter 5.
On 4 January, 2016, John Brown purchased a home for $900,000. He paid a deposit of $200,000 and on the same day borrowed the balance of the purchase price from the ABC Bank at an interest rate of j12 = 6%, that is, at a nominal interest rate of 6% per annum, compounded monthly (12 times a year). He agreed with the bank that the loan was to be repaid over a period of 25 years, by equal monthly instalments of $4,510.11, each instalment consisting of part interest and part principal. Monthly repayments will be made on 4th day of each month over this period, with the first instalment due on 4th February, 2016.
REQUIRED:
You are required to answer the following questions. Show all workings, and show all answers correct to the nearer cent. Accuracy and presentation are important.
(a) Verify the bank's calculation of the monthly instalment of $4,510.11.
(b) Assume that all monthly loan repayments are made on the due date. On 4 January, 2019, after payment of the monthly instalment due that day, what will be the amount of loan still outstanding, that is, remaining to be repaid to the bank? [Assume that interest rates are unchanged.)
(c) Over the following 12 months (ending 4 January, 2020, and including the instalment due on that date), all monthly repayments are made on time. What would be the amount of interest paid over that 12 months period?
(d) Calculate the amount of loan principal to be repaid over the year ending 4 January, 2020, assuming that all instalments are paid on the due dates?
(e) On 4 January, 2020, after repayment of the instalment due that day, mortgage interest rates rise to j2 = 7.2% per annum, that is 7.2% per annum, compounded half-yearly. The bank decides to increase the monthly home loan repayment instalment, so that at the new interest rate, the loan will be completely repaid at the end of the original term. What will be the new monthly repayment instalment?
(f) On learning the amount of the increased instalment (from part (e)), John Brown advises the bank that he cannot afford to pay any increased instalment. The Bank decides to allow John Brown to continue to repay the loan by the same level of monthly repayments, but advises John Brown that the term of the loan will be increased as kit will take longer to repay the Loan. Calculate the time required to repay the loan, in years and months (at the new interest rate) if the loan instalment remains unaltered ($4,510.11).
(g) In part (f), what will be the amount of the final monthly repayment?
(h) Suppose that on 4 January, 2022, loan interest rates rise further to J4 = 9.6% per annum, that is 9.6% per annum, compounded quarterly. John Brown advises the bank that he cannot afford to pay any higher instalment. If the bank agrees to John brown's request, calculate how long it will take before the loan is repaid at the new higher interest rate.
(i) Interpret your answer to part (h). What does it mean? Explain carefully.
(j) Drawing on your knowledge of the Sydney housing market in recent years, advise John Brown and the Bank how they should deal with the situation they are faced with in (h) and (i) above