Investment

Financial Maths, STD2 F4 2025 HSC 23

Company $\text{A}$ and Company $\text{B}$ both issue an annual dividend per share as shown in the table.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} {Company} \rule[-1ex]{0pt}{0pt} & {Current \ share \ price} \rule[-1ex]{0pt}{0pt} & {Annual \ dividend}\\
{} & {} & { per \ share}\\
\hline
\rule{0pt}{2.5ex} \text{A} \rule[-1ex]{0pt}{0pt} & \text{\$25.43} \rule[-1ex]{0pt}{0pt} & \text{\$4.92}\\
\hline
\rule{0pt}{2.5ex} \text{B} \rule[-1ex]{0pt}{0pt} & \text{\$2.13} \rule[-1ex]{0pt}{0pt} & \text{45c}\\
\hline
\end{array}
Based on the dividend yield, which company would be better to invest in? (2 marks)

--- 10 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text{Div yield (A)} =\dfrac{4.92}{25.43}=0.1934 = 19.3\% $

$\text{Div yield (B)} =\dfrac{0.45}{2.13}=0.211 = 21.1\% $

$\text{Since Div yield (B) > Div yield (A), it is better to invest in company B.}$

Show Worked Solution

$\text{Div yield (A)} =\dfrac{4.92}{25.43}=0.1934 = 19.3\% $

$\text{Div yield (B)} =\dfrac{0.45}{2.13}=0.211 = 21.1\% $

$\text{Since Div yield (B) > Div yield (A), it is better to invest in company B.}$

Financial Maths, STD2 F1 2024 NHT1 24*

Jarryd invested $14 000 into an account earning compound interest at a fixed rate per time period.

The graph below shows the balance of the account for four of the first five time periods after the initial investment. The information for time period 3 is not shown.

Immediately after the interest was calculated for time period 3, Jarryd added an extra one-off amount into the account.

Determine the value of Jarrod's extra one off amount, giving your answer correct to the nearest cent. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

$\$224.03 $

Show Worked Solution

$\text{Increase factor between periods}\ = \dfrac{15\,120}{14\,000}=1.08$

$\text{At time period 3:}$

$\text{Balance (before extra payment)}\ = 14\,000 \times 1.08^{3} = 17\,635.97 $

$\text{Let}\ V = 17\,635.97 +\ \text{extra payment}$

$V \times 1.08 = 19\,288.80\ \ \Rightarrow\ \ V=17\,860.00$

$\therefore \ \text{Extra payment}\ = 17\,860.00-17\,635.97=\$224.03 $

v1 Financial Maths, STD2 F4 2024 HSC 7 MC

Four years ago, the price of a laptop was $1,200.

Due to inflation, the price increased annually by 3%.

What is the price of this laptop now?

$1,248.00
$1,349.86
$1,350.61
$1,374.62

Show Answers Only

$C$

Show Worked Solution

$r=3 \%=\dfrac{3}{100}=0.03$

	$FV$	$=PV(1+r)^n$
		$=1200(1.03)^4$
		$=1350.61$

$\Rightarrow C$

v1 Financial Maths, STD2 F4 2023 HSC 10 MC

An amount of $18 000 is invested for five years. Interest is earned at a rate of 6% per annum, compounding monthly.

Which expression gives the value of the investment after 5 years, in dollars?

`18\ 000 xx 1.005^{60}`
`18\ 000 xx 1.06^{5}`
`18\ 000 xx 1.005^{5}`
`18\ 000 xx 1.06^{60}`

Show Answers Only

`A`

Show Worked Solution

`text{Interest rate}\ = 6/12=0.5%\ text{per month}`

`text{Compounding periods}\ = 5xx12=60`

`:.FV=18\ 000 xx 1.005^{60}`

`=>A`

v1 Financial Maths, STD2 F4 2022 HSC 11 MC

In eight years, the future value of an investment will be $120 000. The interest rate is 6% per annum, compounded half-yearly.

Which equation will give the present value `(PV)` of the investment?

`PV=(120\ 000)/((1+0.06)^(8))`
`PV=(120\ 000)/((1+0.03)^(8))`
`PV=(120\ 000)/((1+0.03)^(16))`
`PV=(120\ 000)/((1+0.06)^(16))`

Show Answers Only

`C`

Show Worked Solution

`text{Compounding periods} = 8 xx 2 = 16`

`text{Compounding rate} = (6text{%}) / 2 = 3text{%} = 0.03`

`PV = (120\ 000) / ((1 + 0.03) ^{16})`

`=> C`

Financial Maths, STD2 F1 2024 GEN1 20*

Dainika invested $2000 for three years at 4.4% per annum, compounding quarterly.

To earn the same amount of interest in three years in a simple interest account, determine the annual simple interest rate. Give your as a percentage, correct to two decimal places. (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

$4.68\%$

Show Worked Solution

$\text{Interest rate (per compounding period)} = \dfrac{4.4}{4} = 1.1 \%$

$\text{Compounding periods}\ =3\times4=12$

$FV=PV(1+r)^{n} = 2000(1+0.011)^{12}=$2280.57$

$\text{Annual interest}\ = \dfrac{280.57}{3}=$93.52$

$\text{S.I. rate}\ =\dfrac{93.52}{2000}\times 100\%=4.676\dots=4.68\%\ \text{(2 d.p.)}$

♦ Mean mark 48%.

Financial Maths, STD2 F4 2024 HSC 25

Alex and Jun each invest $1800 for 5 years.

- Alex's investment earns simple interest at a rate of 7.5% per annum.
- Jun's investment earns interest at a rate of 6.0% per annum, compounding quarterly.

By calculating the interest earned over the 5 years, determine who will have the greater amount. (3 marks)

--- 10 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text {Alex’s investment:}$

$\text{Interest}=Prn=1800 \times 0.075 \times 5=\$ 675$

$\text {Jun’s investment:}$

$r=\dfrac{6.0\%}{4}=1.5 \% \text { per quarter}$

$\text {Compounding periods }=5 \times 4=20$

$F V=P V(1+r)^n=1800(1+0.015)^{20}=\$ 2424.34$

$\text{Total interest}=F V-P V=2424.34-1800=\$ 624.34$

$\text {Alex’s interest }>\text { Jun’s interest.}$

$\Rightarrow \text{ Alex will have a greater amount (since original investment the same)}$

Show Worked Solution

$\text {Alex’s investment:}$

$\text{Interest}=Prn=1800 \times 0.075 \times 5=\$ 675$

$\text {Jun’s investment:}$

$r=\dfrac{6.0\%}{4}=1.5 \% \text { per quarter}$

$\text {Compounding periods }=5 \times 4=20$

$F V=P V(1+r)^n=1800(1+0.015)^{20}=\$ 2424.34$

$\text{Total interest}=F V-P V=2424.34-1800=\$ 624.34$

$\text {Alex’s interest }>\text { Jun’s interest.}$

$\Rightarrow \text{ Alex will have a greater amount (since original investment the same)}$

Financial Maths, STD2 F1 2024 HSC 13 MC

José takes out a loan of $9000. Simple interest is charged on the loan.

The loan and the interest charged will be repaid by making monthly repayments of $300 over 4 years.

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

Show Answers Only

$A$

Show Worked Solution

$\text{Number of repayments}=4 \times 12=48$

$\text{Total repayments }=48 \times 300=\$ 14\,400$

$\text{Interest paid}=14\,400-9000=\$ 5400$

	$I$	$=Prn$
	$5400$	$=9000 \times r \times 4$
	$r$	$=\dfrac{5400}{9000 \times4}=0.15$

$\Rightarrow A$

♦ Mean mark 39%.

Financial Maths, STD2 F4 2024 HSC 7 MC

Three years ago, the price of a uniform was $180.

Due to inflation, the price increased annually by 2.5%.

What is the price of this uniform now?

$180.14
$ 181.35
$ 193.50
$ 193.84

Show Answers Only

$D$

Show Worked Solution

$r=2.5 \%=\dfrac{2.5}{100}=0.025$

	$FV$	$=PV(1+r)^n$
		$=180(1.025)^3$
		$=193.84$

$\Rightarrow D$

Financial Maths, STD2 F4 2023 HSC 10 MC

An amount of $25 000 is invested for six years. Interest is earned at a rate of 8% per annum, compounding quarterly.

Which expression gives the value of the investment after 6 years, in dollars?

`25\ 000 xx 1.02^{24}`
`25\ 000 xx 1.02^{6}`
`25\ 000 xx 1.08^{24}`
`25\ 000 xx 1.08^{6}`

Show Answers Only

`A`

Show Worked Solution

`text{Interest rate}\ = 8/2=2%\ text{per quarter}`

`text{Compounding periods}\ = 6xx4=24`

`:.FV=25\ 000 xx 1.02^{24}`

`=>A`

Financial Maths, STD2 F1 2023 HSC 1 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 xx 3/100 xx 2`
	`=$150`

`=>B`

Financial Maths, STD2 F4 2022 HSC 11 MC

In ten years, the future value of an investment will be $150 000. The interest rate is 4% per annum, compounded half-yearly.

Which equation will give the present value `(PV)` of the investment?

`PV=(150\ 000)/((1+0.04)^(10))`
`PV=(150\ 000)/((1+0.04)^(20))`
`PV=(150\ 000)/((1+0.02)^(10))`
`PV=(150\ 000)/((1+0.02)^(20))`

Show Answers Only

`D`

Show Worked Solution

`text{Compounding periods}\ = 10 xx 2 = 20`

`text{Compounding rate}\ = (4text{%})/2 = 2text{%} = 0.02`

`PV=(150\ 000)/((1+0.02)^(20))`

`=>D`

Financial Maths, STD2 F4 2022 HSC 10 MC

Alex purchased 800 shares. The total cost was $2.60 per share. Alex sold the shares one year later for $3.40 each and paid a fee of $24.95 for selling the shares.

What profit did Alex make on these shares?

$590.10
$615.05
$640.00
$664.95

Show Answers Only

`B`

Show Worked Solution

`text{C}text{ost of shares}\ = 800 xx 2.60=$2080`

`text{Sale funds}`	`=\ text{sale price}\ -\ text{fee}`
	`=(800 xx 3.40)-24.95`
	`=2695.05`

`text{Profit}`	`=\ text{Sale funds}\ -\ text{C}text{ost}`
	`=2695.05-2080`
	`= $615.05`

`=>B`

Financial Maths, STD1 F2 2021 HSC 14

It costs $2.45 for a car to travel on a toll road. Due to inflation, the cost is to increase by 3% each year.

How much will it cost for a car to travel on the toll road in 5 years time? (2 marks)

Show Answers Only

`$2.84`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
	`= 2.45(1 + 3/100)^5= 2.45(1.03)^5= $2.84`

Financial Maths, STD2 F4 2021 HSC 30

Ariana owns 1500 shares in a company. The market price for each share is $27. Ariana's total dividend from these shares is $810.

Calculate the dividend yield for her shares. (2 marks)

Show Answers Only

`2text(%)`

Show Worked Solution

♦ Mean mark 47%.

`text(Dividend yield)`	`= text(Dividend)/text(Value of shares)`
	`= 810/(1500 xx 27)`
	`=0.02`
	`= 2 text(% yield)`

Financial Maths, STD2 F4 2021 HSC 26

Nina plans to invest $35 000 for 1 year. She is offered two different investment options.

Option A: Interest is paid at 6% per annum compounded monthly.

Option B: Interest is paid at `r` % per annum simple interest.

Calculate the future value of Nina's investment after 1 year if she chooses Option A. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
Find the value of `r` in Option B that would give Nina the same future value after 1 year as for Option A. Give your answer correct to two decimal places. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$37\ 158.72`
`6.17text(%)`

Show Worked Solution

a.	`r`	`= text(6%)/12= text(0.5%) = 0.005\ text(per month)`
	`n`	`=12`

`FV`	`= PV(1 + r)^n`
	`= 35\ 000(1 + 0.005)^(12)`
	`= $37\ 158.72`

♦♦ Mean mark part (b) 36%.

b.	`I`	`=Prn`
	`2158.72`	`=35\ 000 xx r xx 1`
	`r`	`=2158.72/(35\ 000)`
		`=0.06167…`
		`=6.17 text{% (to 2 d.p.)}`

Financial Maths, STD2 F2 2021 HSC 5 MC

Peter currently earns $21.50 per hour. His hourly wage will increase by 2.1% compounded each year for the next four years.

What will his hourly wage be after four years?

`21.50(1.21)^4`
`21.50(1.021)^4`
`21.50 + 21.50 xx 0.21 xx 4`
`21.50 + 21.50 xx 0.021 xx 4`

Show Answers Only

`B`

Show Worked Solution

`text(Method 1: Successive SI applications)`

`text(Wage after 1 year) = 21.50 xx 1.021`

`text(Wage after 2 years) = 21.50 xx 1.021 xx 1.021 = 21.50(1.021)^2`

`vdots`

`text(Wage after 4 years) = 21.50(1.021)^4`

`text(Method 2: Using FV formula)`

`FV=PV(1+r)^n`

`FV=21.5 xx(1+2.1/100)^4=21.50(1.021)^4`

`=> B`

Financial Maths, STD2 F4 2020 HSC 29

Jana owns a share portfolio. Details of her share portfolio at 30 June 2020 are given in the table.

Jana received a total annual dividend of $149.52 from her share portfolio.

Calculate the number of shares Jana has in company `XYZ` on 30 June 2020. (3 marks)

Show Answers Only

`348`

Show Worked Solution

`ABC \ text{Dividend}`	`= text{Value of shares} xx text{dividend yield}`
	`= (200 xx 5.5) xx 0.06`
	`= $66.00`

♦ Mean mark 43%.

`XYZ \ text{Dividend}`	`= 149.52 – 66.00`
	`= $83.52`

`text{Let} \ \ x = text{number of} \ XYZ \ text{shares}`

`83.52`	`= text{Value of} \ XYZ \ text{shares} xx text{dividend yield}`
`83.52`	`= (x xx 6.0) xx 0.04`
`6x`	`= frac{83.52}{0.04}`
`therefore \ x`	`= frac{2088}{6}`
	`= 348`

Financial Maths, STD2 F4 2020 HSC 21

The inflation rate over the year from January 2019 to January 2020 was 2%.

The cost of a school jumper in January 2020 was $122.

Calculate the cost of the jumper in January 2019 assuming that the only change in the cost of the jumper was due to inflation. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`$119.61`

Show Worked Solution

`FV`	`=PV(1+r)^n`
`122`	`=C_(2019)(1+0.02)^1`
`C_2019 xx 1.02`	`= 122`
`C_2019`	`= frac(122)(1.02)`
	`= $119.61`

Financial Maths, STD2 F4 2020 HSC 4 MC

Joan invests $200. She earns interest at 3% per annum, compounded monthly.

What is the future value of Joan's investment after 1.5 years?

$209.07
$209.19
$279.51
$311.93

Show Answers Only

`B`

Show Worked Solution

`text(Monthly interest rate) \ = frac(0.03)(12)`

`n \ = \ 1.5 xx 12 = 18`

`text(FV)`	`= text(PV) \ (1 + r)^n`
	`= 200 (1 + frac(0.03)(12))^18`
	`= $209.19`

`=> \ B`

Financial Maths, STD2 F4 2019 HSC 13 MC

The graph show the future values over time of `$P`, invested at three different rates of compound interest.

Which of the following correctly identifies each graph?

A.		B.
C.		D.

Show Answers Only

`C`

Show Worked Solution

`text(Values increase quicker)`

`text(- higher compounding interest rate)`

`text(- same rate but more frequent compounding period)`

`:. W = 10text(% quarterly)`

`X = 10text(% annually)`

`Y = 5text(% annually)`

`=> C`

Financial Maths, STD2 F1 2019 HSC 9 MC

What is the interest earned, in dollars, if $800 is invested for `x` months at a simple interest rate of 3% per annum?

`2x`
`24x`
`200x`
`2400x`

Show Answers Only

`A`

Show Worked Solution

♦♦♦ Mean mark 20%!

`text(Interest)`	`= 800 xx x/12 xx 3/100`
	`= 2x`

`=> A`

Financial Maths, STD2 F4 2019 HSC 3 MC

Chris opens a bank account and deposits $1000 into it. Interest is paid at 3.5% per annum, compounding annually.

Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?

$1070.00
$1071.23
$1822.50
$2070.00

Show Answers Only

`=> B`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
	`= 1000(1 + 0.035)^2`
	`= $1071.23`

`=> B`

Financial Maths, STD2 F4 2019 HSC 21

A person owns 1526 shares with a market value of $8.75 per share. The total dividend received for these shares is $1068.20.

Calculate the percentage dividend yield. (2 marks)

Show Answers Only

`8text(%)`

Show Worked Solution

`text(Value of shares)`	`= 1526 xx 8.75`
	`= $13\ 352.50`

`:.\ text(Dividend yield)`	`= 1068.20/(13\ 352.50)`
	`= 0.08`
	`= 8text(%)`

Financial Maths, STD2 F4 2008 HSC 24c

Heidi’s funds in a superannuation scheme have a future value of $740 000 in 20 years time. The interest rate is 4% per annum and earnings are calculated six-monthly.

What single amount could be invested now to produce the same result over the same period of time at the same interest rate? (3 marks)

Show Answers Only

`$335\ 138.91`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
`740\ 000`	`= PV(1 + 2/100)^40`
`:. PV`	`= (740\ 000)/((1.02)^40)`
	`= 335\ 138.907\ …`
	`= $335\ 138.91`

Financial Maths, STD2 F4 SM-Bank 1

An investment fund purchases 4500 shares of Bank ABC for a total cost of $274 500 (ignore any transaction costs).

The investment fund is paid a divided of $3.66 per share in the first year.

What was the purchase price of 1 share? (1 mark)
Calculate the divided yield. (1 mark)

Show Answers Only

`$61`
`text(6%)`

Show Worked Solution

i. `text(Price per share)`

`= (274\ 500)/4500`

`= $61`

ii. `text(Dividend Yield)`

`= text(Dividend)/text(Share Price) xx 100`

`= 3.66/61 xx 100`

`= 6text(%)`

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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`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 F4 2017 HSC 26e

Sam purchased 500 company shares at $3.20 per share. Brokerage fees were 1.5% of the purchase price.

Sam is paid a dividend of 26 cents per share, then immediately sells the shares for $4.80 each.

If he pays no further brokerage fees, what is Sam’s total profit? (3 marks)

Show Answers Only

`$906`

Show Worked Solution

`text(Purchase price)`	`= 500 xx 3.20`
	`= $1600`

`text(Brokerage fees)`	`= 1.5text(%) xx 1600`
	`= $24`

`text(Dividends)`	`= 500 xx 0.26`
	`= $130`

`text(Sale price)`	`= 500 xx 4.80`
	`= $2400`

`:.\ text(Total profit)`	`= 2400 + 130 – (1600 + 24)`
	`= $906`

Financial Maths, STD2 F4 2017 HSC 10 MC

A single amount of $10 000 is invested for 4 years, earning interest at the rate of 3% per annum, compounded monthly.

Which expression will give the future value of the investment?

`10\ 000 xx (1 + 0.03)^4`
`10\ 000 xx (1 + 0.03)^48`
`10\ 000 xx (1 + 0.03/12)^4`
`10\ 000 xx (1 + 0.03/12)^48`

Show Answers Only

`D`

Show Worked Solution

`text(Compounding rate)\ = 3/100 ÷ 12= 0.03/12`

`text(Compounding periods)= 4 xx 12=48`

`:.\ text(FV) = 10\ 000 xx (1 + 0.03/12)^48`

$\Rightarrow D$

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

Show Answers Only

`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 F4 2015 HSC 26d

A family currently pays $320 for some groceries.

Assuming a constant annual inflation rate of 2.9%, calculate how much would be paid for the same groceries in 5 years’ time. (2 marks)

Show Answers Only

`$369.17\ \ text{(nearest cent)}`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
	`= 320(1.029)^5`
	`= $369.1703\ …`
	`= $369.17\ \ text{(nearest cent)}`

Financial Maths, STD2 F4 2015 HSC 17 MC

What amount must be invested now at 4% per annum, compounded quarterly, so that in five years it will have grown to `$60\ 000`?

`$8919`
`$11 156`
`$49\ 173`
`$49\ 316`

Show Answers Only

`C`

Show Worked Solution

`text(Using)\ \ FV = PV(1 + r)^n`

`r= text(4%)/4= text(1%) = 0.01\ text(per quarter)`

`n= 5 xx 4= 20\ text(quarters)`

`60\ 000`	`= PV(1 + 0.01)^(20)`
`:.\ PV`	`= (60\ 000)/1.01^(20)`
	`= $49\ 172.66…`

`⇒ C`

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)

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

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 F4 2005 HSC 13 MC

Last year, Helen bought 150 shares at $2.00 per share. They are now worth $2.50 per share. Helen receives a dividend of $0.10 per share.

What is the dividend yield?

`text(4%)`
`text(20%)`
`$15`
`$75`

Show Answers Only

`A`

Show Worked Solution

`text(Dividend yield)`	`= text(Dividend)/text(Share Value)`
	`= 0.10/2.50`
	`= 0.04`
	`=\ text(4%)`

`=> A`

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)

--- 1 WORK AREA LINES (style=lined) ---
At the end of 6 years, which investment will be worth the most and by how much? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
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)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`$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 F4 2014 HSC 30a

Chandra and Sascha plan to have $20 000 in an investment account in 15 years time for their grandchild’s university fees.

The interest rate for the investment account will be fixed at 3% per annum compounded monthly.

Calculate the amount that they will need to deposit into the account now in order to achieve their plan. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`$12\ 760\ \ text{(nearest $)}`

Show Worked Solution

♦ Mean mark 49%

`FV = $20\ 000,\ \ n = 15xx 12=180,`

`r = 0.03 /12=0.0025`

`FV`	`= PV (1 + r)^n`
`20\ 000`	`=PV (1 + 0.0025)^180`
`PV`	`=(20\ 000)/(1.0025)^180`
	`=12\ 759.73…`

`:.\ text(They need to deposit) \ \ $12\ 760\ \ text{(nearest $)}`

Financial Maths, STD2 F4 2013 HSC 28d

Adhele has 2000 shares. The current share price is $1.50 per share. Adhele is paid a dividend of $0.30 per share.

What is the current value of her shares? (1 mark)
Calculate the dividend yield. (1 mark)

Show Answers Only

`$3000`
`text(20%)`

Show Worked Solution

i.	`text(# Shares)=2000`
	`text(Share price) = $1.50`

`:.\ text(Current value)`	`= 2000 xx 1.50`
	`=$3000`

♦♦♦ Mean mark 13%
MARKER’S COMMENT: A large majority of students had a poor understanding of the term dividend yield.

ii.	`text(Dividend yield)`	`=\ text(Dividend)/text(Share price)`
		`= 0.30/1.50`
		`=20 text(%)`

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 F4 2009 HSC 6 MC

A house was purchased in 1984 for $35 000. Assume that the value of the house has increased by 3% per annum since then.

Which expression gives the value of the house in 2009?

`35\ 000(1 + 0.03)^25`
`35\ 000(1 + 3)^25`
`35\ 000 xx 25 xx 0.03`
`35\ 000 xx 25 xx 3`

Show Answers Only

`A`

Show Worked Solution

`r =\ text(3%)\ = 0.03`

`n = 25\ text(years)`

`text(Using)\ \ FV = PV(1 + r)^n`

` :.\ text(Value in 2009) = 35\ 000(1+0.03)^25`

`=> A`

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`

	\(FV\)	\(=PV(1+r)^n\)
		\(=1200(1.03)^4\)
		\(=1350.61\)

	\(I\)	\(=Prn\)
	\(5400\)	\(=9000 \times r \times 4\)
	\(r\)	\(=\dfrac{5400}{9000 \times4}=0.15\)

	\(FV\)	\(=PV(1+r)^n\)
		\(=180(1.025)^3\)
		\(=193.84\)

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