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Now that they have accumulated a deposit of 55,000 Jack and Jill take out a housing loan to purchase a home. The house costs $755,000. It is to be repaid in equal monthly instalments over a term of 30 years. The interest rate quoted by the bank is an effective annual rate is 7.5%pa. Jack has lost the paperwork showing the annual nominal rate (j12 ) with monthly compounding.

i. How much is the monthly repayment?
ii. How much do Jack and Jill owe the bank immediately before making the 130th repayment?
iii. After making the 150th repayment Jack and Jill receive an amount of $50,000, which they use to reduce their loan. The bank allows them to make the same monthly payment. How much will the term of the loan be reduced by if the interest rate remains the same?


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