smc-1124-10-Simple Interest

Financial Maths, STD1 F1 EQ-Bank 25

Riley borrowed $4000 at a simple interest rate of 6% per annum. The loan is to be repaid as a single lump sum at the end of 8 months.

Calculate the total amount Riley must repay. (2 marks)

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$\$4160$

Show Worked Solution

$\text{Interest}$	$=Prn$
	$=4000\times 0.06\times \dfrac{8}{12}=\$160$

$\therefore\ \text{Total repayment} =4000+160=\$4160$

Financial Maths, STD1 F1 EQ-Bank 22

Olivia borrowed $3600 at 8% per annum.

Calculate the simple interest for the first 5 months. (2 marks)

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$\$120$

Show Worked Solution

$\text{Interest}$	$=Prn$
	$=3600\times 0.08\times \dfrac{5}{12}=\$120$

Financial Maths, STD1 F1 EQ-Bank 5 MC

Chloe invests $5000 for 2 years and 3 months. Simple interest is paid on the investment at a rate of 4% per annum.

What is the total value of the investment at the end of this period?

$450
$5200
$5400
$5450

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$D$

Show Worked Solution

$\text{2 years and 3 months = 27 months}$

$I=Prn=5000 \times 0.04 \times \dfrac{27}{12}=\$450$

$\therefore\ \text{Value of Investment} =5000+450=\$5450$

$\Rightarrow D$

Financial Maths, STD1 F1 EQ-Bank 8 MC

Ava is saving for a trip to Bali. She invests an amount of money at a simple interest rate of 3.5% per annum. After 2 years, she has earned $210 in interest.

How much money did Ava originally invest?

$1470
$2100
$3000
$6000

Show Answers Only

$C$

Show Worked Solution

$I=\$210,\ r=3.5\%=0.035,\ n=2\ \text{years}$

$\text{Using}\ \ I=Prn\ \ \text{to find}\ P:$

$I$	$=Prn$
$P$	$=\dfrac{I}{r \times n}=\dfrac{210}{0.035 \times 2}=\$3000$

$\Rightarrow C$

Financial Maths, STD1 F1 EQ-Bank 4 MC

Liam invests $7500 in a term deposit with Westpac that pays simple interest at a rate of 5% per annum.

How much interest is earned over the first 4 years?

$375
$1125
$1500
$9000

Show Answers Only

$C$

Show Worked Solution

$P=\$7500,\ r=5\%=0.05,\ n=4\ \text{years}$

$I=Prn=7500 \times 0.05 \times 4=\$1500$

$\Rightarrow C$

v1 Financial Maths, STD2 F1 2005 HSC 25a

Reece is preparing his annual budget for 2006.

His expected income is:

• $90 every week as a swimming coach
• Interest earned from an investment of $4500 at a rate of 4% per annum.

His planned expenses are:

• $30 every week on transport
• $12 every week on lunches
• $48 every month on entertainment.

Reece will save his remaining income. He uses the spreadsheet below for his budget.

Determine the values of `X`, `Y` and `Z`. (Assume there are exactly 52 weeks in a year.) (3 marks)

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At the beginning of 2006, Reece starts saving.

Will Reece have saved enough money during 2006 for a deposit of $2500 on a car if he keeps to his budget? Justify your answer with suitable calculations. (2 marks)

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`X =$180, Y = $1560\ text(and) \ Z = $576`
`text(Reece will NOT have saved enough for a $2500deposit.)`

Show Worked Solution

i. `text(Interest on Investment) = X`

`X`	`= 4500 xx 4 text(%)`
	`= $180`

`text(Transport =)\ Y`

`Y`	`= 52 × 30`
	`= $1560`

`text(Entertainment =)\ Z`

`Z`	`= 48 × 12`
	`= $576`

ii.	`text(Total Income)`	`= 4680 + 180`
		`= $4860`

`text(Total Expenses)`	`= 1560 + 624 + 576`
	`= $2760`

`text(Savings)`	`= 4860 − 2760`
	`= $2100`

`:.\ text(Reece will NOT have saved enough for)`

`text(a $2500 deposit.)`

v1 Financial Maths, STD2 F1 2013 HSC 13 MC

Jared borrowed $9 000. He repaid the loan in full at the end of three years with a lump sum of $10 350.

What annual simple interest rate was he charged?

6%
5.25%
5%
4.5%

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`C`

Show Worked Solution

`text(Total interest paid) = 10\ 350-9000 = $1350`

`I`	`=Prn`
`1350`	`=9000 xx r xx 3`
`r`	`=1350/(27\ 000)`
	`=5 text(%)`

`=> C`

v1 Financial Maths, STD2 F1 2010 HSC 5 MC

Lina invests $2500 for 1 year and 2 months. The simple interest is calculated at a rate of 5% per annum.

What is the total value of the investment at the end of this period?

$2700
$2650
$2630
$2800

Show Answers Only

`C`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=2500 xx \text(5%)\ xx 14/12`
	`=$130`

`:.\ text(Value of Investment)`	`=2500+130`
	`=$2630`

`=> C`

Financial Maths, STD1 F1 2024 HSC 21

Jan borrowed $1500 at 6% per annum.

Calculate the simple interest for the first three months. (2 marks)

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$$22.50$

Show Worked Solution

$\text{Interest}$	$=Prn$
	$=1500\times 0.06\times \dfrac{3}{12}=$22.50$

Mean mark 57%.

Financial Maths, STD1 F2 2023 HSC 24

Bobby invested $5000.

The table shows the progress of his investment over the first 4 months.

What are the values of $A$ and $B$? (2 marks)

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Bobby could have earned simple interest on the investment at 0.62% per month.
How much interest would Bobby have earned over 4 months by choosing this option? (2 marks)

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a. $A=$30.54,\ \ B=$5121.08$

b. $$124$

Show Worked Solution

a.	$A$	$=5090.54\times\dfrac{0.6}{100}$
		$=$30.54\text{ (2 d.p.)}$

	$B$	$=5090.54+30.54$
		$=$5121.08$

b. $P=$5000,\ \ r=\dfrac{0.62}{100},\ \ n=4$

$I$	$=Prn$
	$=5000\times \dfrac{0.62}{100}\times 4$
	$=$124$

♦♦ Mean mark (b) 31%.

Financial Maths, STD1 F1 2023 HSC 2 MC

An amount of $2500 is invested at a simple interest rate of 3% per annum.

How much interest is earned in the first two years?

$75
$150
$2575
$2652

Show Answers Only

$B$

Show Worked Solution

$I$	$=Prn$
	$=2500 \times\ \dfrac{3}{100} \times\ 2=$150$

$\Rightarrow B$

Financial Maths, STD1 F1 2019 HSC 16

What is the interest earned when $800 is invested for 7 months at a simple interest rate of 3% per annum? (2 marks)

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`$14`

Show Worked Solution

♦ Mean mark 38%.

`text(Interest)`	`= Prn`
	`= 800 xx 0.03 xx 7/12= $14`

Financial Maths, STD2 F1 EQ-Bank 24

George makes a single deposit of $9000 into an account that pays simple interest.

After 4 years, George's account has a balance of $10 350.

What simple interest rate did George receive on his investment? (2 marks)

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`3.75text(%)`

Show Worked Solution

`text(Interest earned)= 10\ 350-9000= $1350`

`text(Using)\ \ I = Prn,`

`1350`	`= 9000 xx r xx 4`
`:. r`	`= 1350/(4 xx 9000)= 0.0375= 3.75text(%)`

Financial Maths, STD2 F1 EQ-Bank 1 MC

$6000 is invested in an account that earns simple interest at the rate of 3.5% per annum.

The total interest earned in the first four years is

$70
$84
$210
$840

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`D`

Show Worked Solution

`P = 6000,\ \ r = 3.5text(%),\ \ n = 4`

`I`	`= Prn`
	`= 6000 xx 3.5/100 xx 4= 840`

`=> D`

Financial Maths, STD2 F1 2005 HSC 25a

Reece is preparing his annual budget for 2006.

His expected income is:

• $90 every week as a swimming coach
• Interest earned from an investment of $5000 at a rate of 4% per annum.

His planned expenses are:

• $30 every week on transport
• $12 every week on lunches
• $48 every month on entertainment.

Reece will save his remaining income. He uses the spreadsheet below for his budget.

Determine the values of `X`, `Y` and `Z`. (Assume there are exactly 52 weeks in a year.) (3 marks)

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At the beginning of 2006, Reece starts saving.

Will Reece have saved enough money during 2006 for a deposit of $2100 on a car if he keeps to his budget? Justify your answer with suitable calculations. (2 marks)

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a. `X =$200, Y = $1560\ text(and) \ Z = $576`

b. `text(Reece will have saved have saved enough for a $2100 deposit.)`

Show Worked Solution

a. `text(Interest on Investment) (X)=5000 xx 4%= $200`

`text(Transport)(Y)= 52 × 30= $1560`

`text(Entertainment) (Z)= 48 × 12= $576`

b. `text(Total Income)= 4680 + 200= $4880`

`text(Total Expenses)= 1560 + 624 + 576= $2760`

`text(Savings)= 4880-2760= $2120`

`:.\ text(Reece will have saved enough for a $2100 deposit.)`

Financial Maths, STD2 F1 2007 HSC 23a

Lilly and Rose each have money to invest and choose different investment accounts.

The graph shows the values of their investments over time.

How much was Rose’s original investment? (1 mark)

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At the end of 6 years, which investment will be worth the most and by how much? (2 marks)

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Lilly’s investment will reach a value of $20 000 first.
How much longer will it take Rose’s investment to reach a value of $20 000? (1 mark)

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`$5000`
`text(Rose’s is worth $2000 more.)`
`text(It takes Lilly 14 years to reach $20 000 and it takes)`

`text{Rose 1 year longer (15 years) to reach the same value}`

Show Worked Solution

i. `$5000\ text{(} y text(-intercept) text{)}`

ii. `text(After 6 years,)`

`text(Lilly’s investment)`	`= $9000`
`text(Rose’s investment)`	`= $11\ 000`
`:.\ text(Rose’s is worth $2000 more.)`

iii. `text(It takes Lilly 14 years to reach $20 000 and it)`

`text{takes Rose 1 year longer (15 years) to reach the}`

`text(same value.)`

Financial Maths, STD2 F1 2009 HSC 20 MC

Lou bought a plasma TV which was priced at $3499. He paid $1000 deposit and got a loan for the balance that was paid off by 24 monthly instalments of $135.36.

What simple interest rate per annum, to the nearest percent, was charged on his loan?

Show Answers Only

$B$

Show Worked Solution

$\text{Loan = Price}\ -\ \text{Deposit}= 3499-1000= \$2499$

$\text{Total repaid}= 24 \times 135.36= \$3248.64$

$\text{Interest paid}= 3248.64-2499= \$749.64$

♦ Mean mark 34%.
COMMENT: A multi-step question targeting higher bands that can be a time-trap for many students.

$\text{Simple Interest}$	$= Prn$
$749.64$	$= 2499 \times r \times 2$
$\therefore r$	$= \dfrac{749.64}{2 \times 2499}= 0.1499\ …\approx 15\%$

$\therefore B$

Financial Maths, STD2 F1 2010 HSC 5 MC

Minjy invests $2000 for 1 year and 5 months. The simple interest is calculated at a rate of 6% per annum.

What is the total value of the investment at the end of this period?

$2170
$2180
$3003
$3700

Show Answers Only

$A$

Show Worked Solution

$\text{1 year and 5 months = 17 months}$

$I=Prn=2000 \times 6\%\ \times \dfrac{17}{12}=\$170$

$\therefore\ \text{Value of Investment} =2000+170=\$2170$

$\Rightarrow A$

Financial Maths, STD2 F1 2013 HSC 13 MC

Polly borrowed $11 000. She repaid the loan in full at the end of two years with a lump sum of $12 000.

What annual simple interest rate was she charged?

4.17%
4.55%
8.33%
9.09%

Show Answers Only

`B`

Show Worked Solution

`text(Total interest paid)=12\ 000-11\ 000=$1000`

`I`	`=Prn`
`1000`	`=11\ 000 xx r xx2`
`r`	`=1000/(22\ 000)=4.55 text(%)`

`=>\ B`

Financial Maths, STD2 F1 2013 HSC 9 MC

Lynne invests $1000 for a term of 15 months. Simple interest is paid on the investment at a rate of 3.75% per annum.

How much will Lynne's investment be worth at the end of the term?

$1046.88
$1047.09
$1296.88
$1468.75

Show Answers Only

`A`

Show Worked Solution

`I=Prn=1000xx3.75/100xx15/12=$46.88`

`:.\ text(Investment worth)\ = 1000+46.88=$1046.88`

`=>\ A`

\(I\)	\(=Prn\)
\(P\)	\(=\dfrac{I}{r \times n}=\dfrac{210}{0.035 \times 2}=\$3000\)

a.	\(A\)	\(=5090.54\times\dfrac{0.6}{100}\)
		\(=$30.54\text{ (2 d.p.)}\)

	\(B\)	\(=5090.54+30.54\)
		\(=$5121.08\)

\(I\)	\(=Prn\)
	\(=5000\times \dfrac{0.62}{100}\times 4\)
	\(=$124\)

\(\text{Simple Interest}\)	\(= Prn\)
\(749.64\)	\(= 2499 \times r \times 2\)
\(\therefore r\)	\(= \dfrac{749.64}{2 \times 2499}= 0.1499\ …\approx 15\%\)

\(\text{Interest}\)	\(=Prn\)
	\(=4000\times 0.06\times \dfrac{8}{12}=\$160\)

\(\text{Interest}\)	\(=Prn\)
	\(=3600\times 0.08\times \dfrac{5}{12}=\$120\)

\(\text{Interest}\)	\(=Prn\)
	\(=1500\times 0.06\times \dfrac{3}{12}=$22.50\)