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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)
Show Answers Only

a.    `$7500`

b.    `text(20%)`

Show Worked Solution
a.    `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.
  

b.     `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)

Show Answers Only

`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 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)

Show Answers Only

`$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)
Show Answers Only
  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)

Show Answers Only

`$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 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)

Show Answers Only

`$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`
Show Answers Only

`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 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. $1,248.00
  2. $1,349.86
  3. $1,350.61
  4. $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?

  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 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.
 

2UG-2005-25a
 

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

At the beginning of 2006, Reece starts saving.

  1. 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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a.    `X =$180, Y = $1560\ text(and) \ Z = $576`

b.    `text(Reece will NOT have saved enough for a $2500 deposit.)`

Show Worked Solution

a.    `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`

 

b.     `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 2019 HSC 9 MC

What is the interest earned, in dollars, if $1200 is invested for `x` months at a simple interest rate of 4% per annum?

  1. `4x`
  2. `40x`
  3. `400x`
  4. `4800x`
Show Answers Only

`A`

Show Worked Solution

♦♦♦ Mean mark 20%!

`text(Interest)` `= 1200 xx x/12 xx 4/100`
  `= 4x`

`=> A`

v1 Financial Maths, STD2 F1 2024 HSC 13 MC

Alicia takes out a loan of $7500. Simple interest is charged on the loan.

The loan and the interest charged will be repaid by making monthly repayments of $250 over 3 years.

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

  1. 7%
  2. 9%
  3. 12%
  4. 15%
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Number of repayments} = 3 \times 12 = 36\)

\(\text{Total repayments} = 36 \times 250 = \$9000\)

\(\text{Interest paid} = 9000 – 7500 = \$1500\)

  \(I\) \(= Prn\)
  \(1500\) \(= 7500 \times r \times 3\)
  \(r\) \(= \dfrac{1500}{7500 \times 3} = 0.0666…\)
    \(= 6.67\% \approx 7\%\)

 
\(\Rightarrow A\)

♦ Mean mark 39%.

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?

  1. 6%
  2. 5.25%
  3. 5%
  4. 4.5%
Show Answers Only

`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?

  1. $2700
  2. $2650
  3. $2630
  4. $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`