smc-1140-20-P+I-R Tables

Financial Maths, STD1 F3 2021 HSC 27

Tracy takes out a 30-year reducing balance loan of $680 000 to buy a house. Interest is charged at 0.25% per month. The loan is to be repaid in equal monthly instalments of $2866.91 over a term of 30 years.

Part of a spreadsheet used to model the reducing balance loan is shown.

Find the amount owing at the end of the second month. (2 marks)

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Suppose that the interest rate reduces to 0.15% per month and the monthly instalments remain as $2866.91.
What will happen to the term of the loan? Explain your answer without using calculations. (2 marks)

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Show Answers Only

`$677\ 663.26`
`text(Loan term will decrease.)`
`text(The repayment will pay down more of the principal each)`
`text(month, reducing the term of the loan.)`

Show Worked Solution

a. `text(In month 2:)`

♦♦ Mean mark part (a) 31%.

`text(Interest) = 678\ 833.09 xx 0.0025 = $1697.08`

`text(Repayment) = $2866.91`

`text(Balance owing)`	`= 678\ 833.09 + 1697.08 – 2866.91`
	`= $677\ 663.26`

b. `text(The term of the loan will decrease.)`

♦♦♦ Mean mark part (b) 18%.

`text(If interest rate reduces, the monthly interest amount)`

`text(payable decreases.)`

`text(The repayment will pay down more of the principal each)`

`text(month, reducing the term of the loan.)`

Financial Maths, STD1 F3 2020 HSC 30

Colin takes out a 5-year reducing balance loan of $19 000 with interest charged at 6% per annum. He uses this money to buy a car valued at $19 000.

The table shows some of the output from a spreadsheet used to model the reducing balance loan.

Colin's car is depreciated using the declining-balance method, with a depreciation rate of 20% per annum.

At the end of 3 years, after making the third repayment on the loan, Colin sells the car at its salvage value. He uses the money from the sale of the car to repay the amount owing on the loan at the end of the third year.

How much money will he have left over? (4 marks)

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`$1458.43`

Show Worked Solution

`V_0 = 19\ 000 \ , \ r = 20text(%) \ , \ n=3`

♦ Mean mark 23%.

`S`	`= V_0 (1 – r)^n`
	`= 19\ 000 (1 – 0.2)^3`
	`= $9728`

`text{Find the amount owing on the loan after 3 years:}`

`text(Using the table,)`

`text{Interest (year 3)} = 0.06 xx 12\ 056.70 = $ 723.40`

`text{Amount owing (end of year 3)`

`= 12\ 056.70 + 723.40 – 4510.53`

`= $ 8269.57`

`therefore \ text{Money left over}`

`= 9728 – 8269.57`

`= $1458.43`

Financial Maths, STD2 F4 2016 HSC 27d

Marge borrowed $19 000 to buy a used car. Interest on the loan was charged at 4.8% pa at the end of each month. She made a repayment of $436 at the end of every month. The table below sets out her monthly repayment schedule for the first four months of the loan.

Some values in the table are missing. Write down the values for `A` and `B`. (2 marks)

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Calculate the value of `X`. (2 marks)

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Marge repaid this loan over four years.

What is the total amount that Marge repaid? (1 mark)

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`A = $19\ 000,quadB = $17\ 551.33`
`$74.56`
`$20\ 928`

Show Worked Solution

i.	`A + 76-436`	`= 18\ 640`
	`:. A`	`= $19\ 000`

`17\ 915.67 + 71.66-436 = B`

`:. B = $17\ 551.33`

ii. `18\ 640 + X-436 = 18\ 278.56`

`:. X`	`= 18\ 278.56 + 436-18\ 640`
	`= $74.56`

♦♦ Mean mark part (iii) 28%.
COMMENT: Read carefully whether total paid or total interest paid is required.

iii. `text(Total amount repaid)`

`= 48 xx 436`

`= $20\ 928`

Financial Maths, STD2 F4 2011 HSC 22 MC

Ying borrowed $250 000 to buy a house. The interest rate and monthly repayment for her loan are shown in the spreadsheet.

What is the total interest charged for the first four months of this loan?

$6364.32
$6366.11
$6369.67
$6376.25

Show Answers Only

`A`

Show Worked Solution

`text(Month 3)`

`P+I-R`	`=251\ 032.04-1871.94`
	`=249\ 160.10`

`text(Month 4)`

`P`	`=249\ 160.10`
`:.I`	`=249\ 160.10xx0.0765/12`
	`=1588.40`

`:.\ text(Total interest)`	`=1593.75+1591.98+1590.19+1588.40`
	`=6364.32`

`=> A`

Financial Maths, STD2 F4 2009 HSC 26c

Margaret borrowed $300 000 to buy an apartment. The interest rate is 6% per annum, compounded monthly. The repayments were set by the bank at $2200 per month for 20 years.

The loan balance sheet shows the interest charged and the balance owing for the first month.

What is the total amount that is to be paid for this loan over the 20 years? (1 mark)

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Find the values of `A` and `B`. (2 marks)

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`$528\ 000`
`A = $1496.50, B = $298\ 596.50`

Show Worked Solution

♦ Mean mark 39%
MARKER’S COMMENT: 1 mark allocation flags the answer should not be too involved.

i. `text(Monthly repayment) = $2200`

`text(# Repayments)\ = 20 xx 12 = 240`

`:.\ text(Total paid)`	`= 2200 xx 240`
	`= $528\ 000`

ii. `text(Interest rate monthly)\ = text(6%)/12=\ text(0.5%)`

`A`	`= text(Principal at start of month) xx 0.5/100`
	`= 299\ 300 xx 0.5/100`
	`= $1496.50`

`B`	`=\ text(Principal + interest – repayment)`
	`= 299\ 300 + 1496.50\-2200`
	`= $298\ 596.50`