smc-603-20-Flat rate loans

CORE*, FUR2 2007 VCAA 1

Khan wants to buy some office furniture that is valued at $7000.

i. A store requires 25% deposit. Calculate the deposit. (1 mark)

The balance is to be paid in 24 equal monthly instalments. No interest is charged.

ii. Determine the amount of each instalment. Write your answer in dollars and cents. (1 mark)

Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of $220.

i. Determine the total amount paid for the furniture at this store. (1 mark)
ii. Calculate the annual flat rate of interest charged by this store.

Write your answer as a percentage correct to one decimal place. (2 marks)

A third store has the office furniture marked at $7000 but will give 15% discount if payment is made in cash at the time of sale.

Calculate the cash price paid for the furniture after the discount is applied. (1 mark)

Show Answers Only

i. `$1750`
ii.`$218.75`
i. `$8420`
ii. `7.3text{%}`
`$5950`

Show Worked Solution

a.i.	`text(Deposit)`	`= 25text(%) xx 7000`
		`= $1750`

a.ii. `text(Installment amount)`

`= ((7000 – 1750))/24`

`= $218.75`

b.i.	`text(Total paid)`	`= 500 + 36 xx 220`
		`= $8420`

b.ii. `text(Total interest paid)`

`= 8420 – 7000`

`= $1420`

`I`	`= (PrT)/100`
`1420`	`= (6500 xx r xx 3)/100`
`:. r`	`= (1420 xx 100)/(6500 xx 3)`
	`= 7.282…`
	`= 7.3text{% (1 d.p.)}`

c.	`text(Cash price)`	`= 7000 – 15text(%) xx 7000`
		`= 7000 – 1050`
		`= $5950`

CORE*, FUR2 2009 VCAA 2

Rebecca will need to borrow $250 to buy a golf bag.

If she borrows the $250 on her credit card, she will pay interest at the rate of 1.5% per month.

Calculate the interest Rebecca will pay in the first month.

Write your answer correct to the nearest cent. (1 mark)
If Rebecca borrows the $250 from the store’s finance company she will pay $6 interest per month.

Calculate the annual flat interest rate charged. Write your answer as a percentage correct to one decimal place. (1 mark)

Show Answers Only

`$3.75`
` text(28.8%)`

Show Worked Solution

a. `text(Interest in the 1st month)`

`= 1.5text(%) xx 250`

`= $3.75`

b. `text(Annual interest) = 12 xx 6 = $72`

`:.\ text(Annual flat interest rate)`

`= 72/250 xx 100text(%)`

`= 28.8text(%)`

CORE*, FUR1 2009 VCAA 3 MC

Jamie bought a $500 games console on a hire-purchase plan.

He paid $50 deposit and monthly instalments of $25 for two years.

The flat interest rate charged per annum is closest to

A. 15.0%

B. 16.7%

C. 30.0%

D. 33.3%

E. 66.7%

Show Answers Only

`B`

Show Worked Solution

`text(Total owing)`	`= 500 − text(deposit)`
	`= 500 − 50`
	`= 450`

`text(Total paid in instalments)`

♦ Mean mark 44%.

`= $25 xx 12\ text(months) xx 2\ text(years)`

`= 600`

`:.\ text(Interest paid)`	`= 600 − 450`
	`= 150`

`I`	`= (PrT)/100`
`150`	`= ((450)(r)(2))/100`
`:. r`	`= (150 xx 100)/(450 xx 2)`
	`= 16.66… %`

`=> B`

CORE*, FUR1 2009 VCAA 2 MC

An amount of $6500 is borrowed at a simple interest rate of 3.5% per annum.

The total interest paid over the period of the loan is $910.

The period of the loan is closest to

A. 2.5 years.

B. 3.5 years.

C. 3.8 years.

D. 4 years.

E. 4.9 years.

Show Answers Only

`D`

Show Worked Solution

`I = 910, \ P = 6500, \ r = 3.5`

`I`	`= (PrT)/100`
`910`	`= ((6500)(3.5)(T))/100`
`:. T`	`= (910 xx 100)/(6500xx3.5)`
	`= 4\ \ text(years)`

`=> D`

CORE*, FUR1 2013 VCAA 4 MC

The purchase price of a car is $15 000.

A deposit of $3000 is paid and the balance will be repaid with 36 monthly payments of $400.

The annual flat rate of interest charged is closest to

A. 1.3%

B. 4.0%

C. 5.3%

D. 6.7%

E. 20.0%

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 49%.

`text(Amount owing)`	`= 15 000 – 3 000`
	`= 12000`

`text(Total interest)`	`= (36 xx 400) – 12000`
	`= 2400`

`I`	`= (PrT) / 100`
`2400`	`= (12000 xx r xx 3) / 100`
`:.r`	`= (2400 xx 100) / `
	`= 6.666…`
	`~~ 6.7text(%)`

`=> D`