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A couple borrows $520,000 to buy a house at 8% per annum over 25 years - HSC - SSCE Mathematics Standard - Question 29 - 2023 - Paper 1

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A couple borrows $520,000 to buy a house at 8% per annum over 25 years. How much does the couple repay in total for this loan? Chris borrows some money at 7% per a... show full transcript

Worked Solution & Example Answer:A couple borrows $520,000 to buy a house at 8% per annum over 25 years - HSC - SSCE Mathematics Standard - Question 29 - 2023 - Paper 1

Step 1

How much does the couple repay in total for this loan?

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Answer

First, we need to find the monthly repayment amount for the loan using the provided table for an interest rate of 8% over 25 years. From the table, the factor for 8% and 25 years is found to be 7.72.

Calculating the monthly repayment:

Amount repaid per month:

ext{Monthly repayment} = 520000 imes rac{7.72}{1000} = 4014.40

Now we calculate the total amount repaid over 25 years:

Total amount repaid:

extTotalrepaid=4014.40imes12imes25=1204320 ext{Total repaid} = 4014.40 imes 12 imes 25 = 1204320

Step 2

How much money does Chris borrow?

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Answer

To find out how much Chris borrows, we can rearrange the payment formula. The monthly repayment is $359.6 at an interest rate of 7% over 15 years. The factor for 7% and 15 years is approximately 8.99.

Using the repayment formula:

Amount borrowed:

extAmountborrowed=359.6imes1000+(8.99imes1000) =4000 ext{Amount borrowed} = 359.6 imes 1000 + (8.99 imes 1000)\ = 4000

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