smc-603-30-Hire purchase

CORE*, FUR2 2010 VCAA 1

The cash price of a large refrigerator is $2000.

A customer buys the refrigerator under a hire-purchase agreement.

She does not pay a deposit and will pay $55 per month for four years.
1. Calculate the total amount, in dollars, the customer will pay. (1 mark)
2. Find the total interest the customer will pay over four years. (1 mark)
3. Determine the annual ﬂat interest rate that is applied to this hire-purchase agreement.
  Write your answer as a percentage. (1 mark)
Next year the cash price of the refrigerator will rise by 2.5%.

The following year it will rise by a further 2.0%.

Calculate the cash price of the refrigerator after these two price rises. (1 mark)

Show Answers Only

i. `$2640`
ii. `$640`
iii. `text(8%)`
`$2091`

Show Worked Solution

a.i. `text(Total amount paid)`

`= 55 xx 4 xx 12`

`= $2640`

a.ii.	`text(Total interest)`	`= 2640-2000`
		`= $640`

a.iii.	`I`	`= (PrT)/100`
	`640`	`= (2000 xx r xx 4)/100`
	`:. r`	`= (640 xx 100)/(2000 xx 4)`
		`= 8text(%)`

b. `text(After 1 year,)`

`P = 2000(1.025) = $2050`

`text(After 2 years,)`

`P = 2050(1.02) = $2091`

CORE*, FUR2 2013 VCAA 3

Hugo paid $7500 for a second bike under a hire-purchase agreement.

A flat interest rate of 8% per annum was charged.

He will fully repay the principal and the interest in 24 equal monthly instalments.

Determine the monthly instalment that Hugo will pay.

Write your answer in dollars, correct to the nearest cent. (2 marks)
Find the effective rate of interest per annum charged on this hire-purchase agreement.

Write your answer as a percentage, correct to two decimal places. (1 mark)
Explain why the effective interest rate per annum is higher than the flat interest rate per annum. (1 mark)
The value of his second bike, purchased for $7500, will be depreciated each year using the reducing balance method of depreciation.

One year after it was purchased, this bike was valued at $6375.

Determine the value of the bike five years after it was purchased.

Write your answer, correct to the nearest dollar. (2 marks)

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`$362.50`
`15.36text(%)`
`text(Simple interest does not take the)`
`text(reducing balance over the life)`
`text(of the loan into account.)`
`$3328\ \ text{(nearest dollar)}`

Show Worked Solution

a.	`text(Total interest)`	`= (PrT)/100`
		`= (7500 xx 8 xx 2)/100`
		`= $1200`

`:.\ text(Total to repay)`	`= 7500 + 1200`
	`= $8700`

`:.\ text(Repayments)`	`= 8700/24`
	`= $362.50`

♦ Mean mark of all parts combined was 37%.

b.	`text(Effective Rate)`	`= (2n)/(n + 1) xx text(flat rate)`
		`= (2 xx 24)/(24 + 1) xx 8`
		`= 15.36text(%)`

c. `text(Simple interest does not take the reducing)`

`text(balance over the life of the loan into account.)`

d.	`text(Depreciation Rate)`	`= 1 – 6375/7500`
		`= 0.15`
		`= 15text(%)`

`:.\ text(Value after 5 years)`

`= 7500 (1 – 0.15)^5`

`= 7500(0.85)^5`

`= 3327.789…`

`= $3328\ \ text{(nearest dollar)}`

CORE*, FUR1 2010 VCAA 1 MC

Sally purchased an electronic game machine on hire purchase. She paid $140 deposit and then $25.50 per month for two years.

The total amount that Sally paid is

A. $191

B. $446

C. $612

D. $740

E. $752

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`E`

Show Worked Solution

`text(Total paid)`	`= 140 + 25.50 xx 2 xx12`
	`= $752`

`=>E`

CORE*, FUR1 2008 VCAA 4-5 MC

Sandra has purchased a $4200 plasma television under a hire-purchase agreement. She paid $600 deposit and will pay the balance in equal monthly instalments over one year.

A flat interest rate of 6% per annum is charged.

Part 1

The amount of each monthly instalment is

`$300`
`$303`
`$318`
`$350`
`$371`

Part 2

The annual effective interest rate that Sandra pays under this agreement is closest to

`10text(%)`
`11text(%)`
`12text(%)`
`13text(%)`
`14text(%)`

Show Answers Only

`text(Part 1:)\ C`

`text(Part 2:)\ B`

Show Worked Solution

`text(Part 1)`

`text(Balance owing)`

`= 4200-600=$3600`

`text(Interest)`

`= 6text(%) xx 3600=$216`

`text(Total need to be repaid)`

`= 3600 + 216`

`= $3816`

`text(Monthly instalment)`

`= 3816/12=$318`

`=> C`

`text(Part 2)`

`r_text(effective)`	`= (100I)/(Pt) xx (2n)/(n + 1)`
	`= (100(216))/(3600 xx 1) xx (2 xx 12)/(12 + 1)`
	`= 11.076…%`

`=> B`

CORE*, FUR1 2007 VCAA 8 MC

Brad investigated the cost of buying a $720 washing machine under a hire purchase agreement.

A deposit of $180 is required and the balance will be paid in 24 equal monthly repayments.

A flat interest rate of 12% per annum applies to the balance.

Brad correctly calculated the monthly repayment to be

A. $22.50

B. $25.20

C. $26.10

D. $27.90

E. $29.70

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`D`

Show Worked Solution

♦ Mean mark 36%.

`text(Amount owing`	`= 720 − 180`
	`= $540`

`I`	`= (PrT)/100`
	`=(540 xx 12 xx2)/100`
	`=$129.60`

`:. \ text(Total Amount Owed)`	`= 129.60 + 540`
	`= $669.60`

`:. \ text(Monthly repayments)\ =669.60/24=$27.90`

`=> D`

CORE*, FUR1 2006 VCAA 6 MC

A $2000 lounge suite was sold under a hire-purchase agreement.

A deposit of $200 was paid.

The balance was to be paid in 36 equal monthly instalments of $68.

The annual flat rate of interest applied to this agreement is

A. 10.0%

B. 11.4%

C. 12.0%

D. 22.4%

E. 36.0%

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`C`

Show Worked Solution

`text(Amount owing)`	`= 2000 − 200`
	`= $1800`

`text(Total amount of instalments)`

`= 68 xx 36`

`= $2448`

`:.\ text(Interest paid)`	`= 2448 − 1800`
	`= $648`

`I`	`= (PrT)/100`
`648`	`= (1800 xx r xx 3)/100`
`:.r`	`= (648 xx 100)/(1800 xx 3)`
	`= 12text(% p.a.)`

`=> C`

CORE*, FUR1 2011 VCAA 6 MC

Shaun decides to buy a new sound system on a time-payment (hire-purchase) plan.

The sound system is priced at $3500.

Shaun pays a deposit of $500 and repayments of $80 per month for five years.

The flat rate of interest charged per annum, correct to one decimal place, is

A. 6.0%

B. 8.7%

C. 10.3%

D. 12.0%

E. 15.3%

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 43%.

`text(Amount owing)`	`= 3500 – 500`
	`= 3000`

`text(Total repayment)`	`= 80 xx 5 xx 12`
	`= 4800`

`text(Interest paid)`	`= 4800 – 3000`
	`= 1800`

`text(Using)\ \ I`	`= (PrT) / 100`
`1800`	`= (3000 xx r xx 5) / 100`
`r`	`= (1800 xx 100) / (3000 xx 5)`
	`= 12.0`

`:.\ text(Rate) = 12text(%)`

`=> D`