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v1 Financial Maths, STD2 F4 2013 HSC 28d

James has 3000 shares. The current share price is  $2.50  per share. James is paid a dividend of  $0.50  per share. 

  1. What is the current value of his shares?   (1 mark)
  2. Calculate the dividend yield.    (1 mark)
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  1. `$7500`
  2. `text(20%)`
Show Worked Solution
i.    `text(# Shares)=3000`
  `text(Share price) = $2.50`

 

`:.\ text(Current value)` `= 3000x 2.50`
  `=$7500`
♦♦♦ 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)`
    `= 0.50/2.50`
    `=20 text(%)`

v1 Financial Maths, STD2 F4 2021 HSC 30

Dianne owns 1600 shares in a company. The market price for each share is $30. Dianne's total dividend from these shares is $768.

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

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`1.6 text(%)`

Show Worked Solution

♦ Mean mark 47%.
`text(Dividend yield)` `= text(Dividend)/text(Value of shares)`  
  `= 768/(1600xx 30)`  
  `=0.016`  
  `= 1.6 text(% yield)`  

v1 Financial Maths, STD2 F4 2013 HSC 26e

Lucas invests $5000.

Interest is compounded half-yearly at a rate of 3% per half-year.

2013 26e

Use the table to calculate the value of his investment at the end of 4 years.   (2 marks)

 

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`$6335`

Show Worked Solution
♦ Mean mark 44%
COMMENT: Structure your answer: 1-Find the interest rate per compounding period (same in this case). 2-Find the number of compounding periods..

`r =\ text(3% per half-year)`

`n = 8 \ \ \ \  text{(8 half-years in 4 years)}`

`⇒ \text{Table Factor} = 1.267`

`text(Investment)` `= 5000 × 1.267`
  `= $6335`

`:.\ \text{After 4 years, investment value is } $6335`

v1 Financial Maths, STD2 F4 2014 HSC 30a

Jordan wants to accumulate $15 000 in a savings account over 10 years to buy a new car.

The account pays interest at 4% per annum compounded monthly.

Calculate how much Jordan must deposit now to achieve this goal. (3 marks)

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`$10\ 110\ \ \text{(nearest $)}`

Show Worked Solution
♦ Mean mark 52%

`FV = 15\ 000,\ \ n = 10 \times 12 = 120,`

`r = 0.04 / 12 = 0.003333…`

`FV` `= PV (1 + r)^n`
`15\ 000` `= PV (1 + 0.003333…)^{120}`
`PV` `= \frac{15\ 000}{(1.003333…)^{120}}`
  `= 10\ 109.88…`

`∴ \ \text{Jordan must deposit} \ $10\ 110\ \text{(nearest $)}`

v1 Financial Maths, STD2 F4 2021 HSC 26

Mila plans to invest $42 000 for 1.5 years. She is offered two different investment options.

Option A:  Interest is paid at 5% per annum compounded monthly.

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

  1. Calculate the future value of Mila's investment after 1.5 years if she chooses Option A. (2 marks)
  2. Find the value of `r` in Option B that would give Mila the same future value after 1.5 years as for Option A. Give your answer correct to two decimal places. (2 marks)
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  1. `$45\ 264.08`
  2. `5.18text(%)`
Show Worked Solution
a.   `r` `= text(5%)/12 = text(0.4167%) = 0.004167\ \text(per month)`
  `n` `= 12 × 1.5 = 18`
`FV` `= PV(1 + r)^n`
  `= 42\ 000(1 + 0.004167)^{18}`
  `= $45\ 264.08`

 

b.   `I` `= Prn`
  `3\ 264.08` `= 42\ 000 × r × 1.5`
  `r` `= 3\ 264.08 / (42\ 000 × 1.5)`
    `= 0.0518…`
    `= 5.18\ \text{% (to 2 d.p.)}`

v1 Financial Maths, STD2 F4 2024 HSC 25

Priya and Leo each invest $2500 for 6 years.

    • Priya's investment earns simple interest at a rate of 5.8% per annum.
    • Leo's investment earns interest at a rate of 4.5% per annum, compounding half-yearly.

By calculating the interest earned over the 6 years, determine who will have the greater amount.   (3 marks)

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\(\text{Priya’s investment:}\)

\(\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870\)

 

\(\text{Leo’s investment:}\)

\(r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}\)

\(\text{Compounding periods} = 6 \times 2 = 12\)

\(FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83\)

\(\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83\)

 

\(\text{Priya’s interest } > \text{ Leo’s interest.}\)

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

Show Worked Solution

\(\text{Priya’s investment:}\)

\(\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870\)

 

\(\text{Leo’s investment:}\)

\(r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}\)

\(\text{Compounding periods} = 6 \times 2 = 12\)

\(FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83\)

\(\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83\)

 

\(\text{Priya’s interest } > \text{ Leo’s interest.}\)

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

v1 Financial Maths, STD2 F4 2015 HSC 26d

A laptop currently costs $850.

Assuming a constant annual inflation rate of 3.2%, calculate the cost of the same laptop in 4 years’ time.  (2 marks)

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`$962.38\ \text{(nearest cent)}`

Show Worked Solution
`FV` `= PV(1 + r)^n`
  `= 850(1.032)^4`
  `= 850(1.132216)`
  `= 962.3836…`
  `= $962.38\ \text{(nearest cent)}`

v1 Financial Maths, STD2 F4 2018 HSC 19 MC

The table shows the compounded values of $1 at different interest rates over different periods.
 

 
Ben hopes to have $18 000 in 2 years to travel. He opens an account today which pays interest of 4% p.a., compounded quarterly.

Using the table, which expression calculates the minimum single sum that Ben needs to invest today to ensure he reaches his savings goal?

  1. 18 000 × 1.0816
  2. 18 000 ÷ 1.0816
  3. 18 000 × 1.0829
  4. 18 000 ÷ 1.0829
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`text(D)`

Show Worked Solution

`text(4% annual)`

`= (4%)/4 = 1% per quarter`

`2 \ text(years) = 8 \ text(periods)`

`\text(From the table: at 8 periods and 1%, compounded value) = 1.0829`.

`:.\ text(Minimum sum) = 18\ 000 ÷ 1.0829`

`=>\ text(D)`

v1 Financial Maths, STD2 F4 2008 HSC 24c

Daniel’s funds in a retirement account are projected to have a future value of $600 000 in 15 years’ time. The interest rate is 5% per annum, with earnings 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)

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`$288\ 629.97`

Show Worked Solution
`FV` `= PV(1 + r)^n`
`600\ 000` `= PV(1 + 2.5/100)^30`
`:. PV` `= (600\ 000)/((1.025)^30)`
  `= 288\ 629.966…`
  `= $288\ 629.97`

v1 Financial Maths, STD2 F4 2005 HSC 13 MC

Two years ago, Jordan bought 200 shares at $3.00 per share. They are now worth $3.75 per share. Jordan receives a dividend of $0.15 per share.

What is the dividend yield?

  1.    `text(3.75%)`
  2.    `text(4%)`
  3.    `text(4.5%)`
  4.    `$30`
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`B`

Show Worked Solution
`text(Dividend yield)` `= text(Dividend)/text(Share Value)`
  `= 0.15/3.75`
  `= 0.04`
  `= 4 text(%)`

`=> B`

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?

  1. `18\ 000 xx 1.005^{60}`
  2. `18\ 000 xx 1.06^{5}`
  3. `18\ 000 xx 1.005^{5}`
  4. `18\ 000 xx 1.06^{60}`
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`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?

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

v1 Financial Maths, STD2 F4 2016 HSC 8 MC

The table shows the future value of an investment of $1000, compounding yearly, at varying interest rates for different periods of time.
 

2ug-2016-hsc-8-mc 

 
Based on the information provided, what is the future value of an investment of $3500 over 5 years at 2% pa?

  1.    $1554.80
  2.    $2835.72
  3.    $3864.28
  4.    $4312.36
0

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`=> C`

Show Worked Solution

`text(Table factor) = 1104.08`

`:. FV` `= 3.5 xx 1104.08`
  `= $3864.28`

 
`=> C`