A young professional couple buy a house for $600,000. They make a down payment of $60,000...

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A young professional couple buy a house for $600,000. They makea down payment of $60,000 and agree to amortise the rest of thedebt with quarterly payments made at the end of each quarter overthe next 20 years. The interest on the debt is 12% per annumcompounded quarterly.
5(a). (i) What type of annuity is this?
(ii) How many payments are made in total?
(iii) What is the interest rate per period?
(iv) Write down an explicit expression for the quarterlypayments.
(v) Determine the amount of each payment (to the nearestdollar).
5(b). Determine the sum of all the payments including the downpayment. (Give your answer to the nearest $100.)
5(c). Explain why the total amount of interest the couple willpay is $890,400 (to the nearest $100).
5(d). Give an expression for the unpaid balance of this loanafter 12 years, and give the value of the unpaid balance (to thenearest $100)

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5 a Purchase Price 600000 Down Payment 60000 Borrowing 600000 60000 540000 Repayment Frequency Quarterly Tenure 20 years or 4 x 20 80 quarters Interest Rate 12 per annum or 124 3 per quarter i See Answer

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A young professional couple buy a house for $600,000. They makea down payment of $60,000 and agree to amortise the rest of thedebt with quarterly payments made at the end of each quarter overthe next 20 years. The interest on the debt is 12% per annumcompounded quarterly.5(a). (i) What type of annuity is this?(ii) How many payments are made in total?(iii) What is the interest rate per period?(iv) Write down an explicit expression for the quarterlypayments.(v) Determine the amount of each payment (to the nearestdollar).5(b). Determine the sum of all the payments including the downpayment. (Give your answer to the nearest $100.)5(c). Explain why the total amount of interest the couple willpay is $890,400 (to the nearest $100).5(d). Give an expression for the unpaid balance of this loanafter 12 years, and give the value of the unpaid balance (to thenearest $100)