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Financial Maths, 2ADV M1 2025 HSC 20

The table shows future value interest factors for an annuity of $1.

Lin invests a lump sum of $21 000 for 7 years at an interest rate of 6% per annum, compounding monthly.

Yemi wants to achieve the same future value as Lin by using an annuity. Yemi plans to deposit a fixed amount into an investment account at the end of each month for 7 years. The investment account pays 6% per annum, compounding monthly.

Using the table provided, determine how much Yemi needs to deposit each month.   (3 marks)

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\($306.78\)

Show Worked Solution

\(r=\dfrac{0.06}{12}=0.005, \ n=12 \times 7=84\)

\(\text{Lin’s investment:}\)

\(F V=21\,000(1+0.005)^{84}=31\,927.76\)
 

\(\text{Yemi’s investment:}\)

\(\text{Annuity factor:} \ 104.07393\)

\(\text{Annuity} \times 104.07393\) \(=$31\,927.76\)
\(\text{Annuity}\) \(=\dfrac{31\,927.76}{104.07393}=$306.78\)

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 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 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`

Financial Maths, 2ADV M1 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)

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\(\$224.03 \)

Show Worked Solution

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

\(\text{At time period 3:}\)

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

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

\(V \times 1.08 = 19\,288.80\ \ \Rightarrow\ \ V=17\,860.00\)

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

Financial Maths, 2ADV M1 2021 HSC 25

A table of future value interest factors for an annuity of $1 is shown.
 

   

Simone deposits $1000 into a savings account at the end of each year for 8 years. The interest rate for these 8 years is 0.75% per annum, compounded annually.

After the 8th deposit, Simone stops making deposits but leaves the money in the savings account. The money in her savings account then earns interest at 1.25% per annum, compounded annually, for a further two years.

Find the amount of money in Simone's savings account at the end of ten years.  (3 marks)

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`$8419.81`

Show Worked Solution

`text(In 1st 8 years:)`

Mean mark 52%.

`text(Future value factor = 8.2132)`

`text(Value of annuity)` `= 8.2132 xx 1000`
  `= $8213.20`
 
`text(After 10 years:)` 
`text(Value of investment)` `= 8213.2 xx (1.0125)^2`
  `= $$8419.81`

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?

  1. `21.50(1.21)^4`
  2. `21.50(1.021)^4`
  3. `21.50 + 21.50 xx 0.21 xx 4`
  4. `21.50 + 21.50 xx 0.021 xx 4`
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`B`

Show Worked Solution

`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`

`=>  B`

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?

  1. $1070.00
  2. $1071.23
  3. $1822.50
  4. $2070.00
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`=> B`

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

 
`=> B`

Financial Maths, STD2 F5 2013 23 MC

Zina opened an account to save for a new car. Six months after opening the account, she made first deposit of $1200 and continued depositing $1200 at the end of each six month period. Interest was paid at 3% per annum, compounded half-yearly.

How much was in Zina's account two years after first opening it?

  1. $4909.08
  2. $4982.72
  3. $5018.16
  4. $5094.55
Show Answers Only

`A`

Show Worked Solution

`text(Interest: 3% p.a ⇒ 1.5% per 6 months)`

♦ Mean mark 41%.

`text(After 2 years,)`

`text(Value of 1st deposit) = 1200(1.015)^3 = 1254.81`

`text(Value of 2nd deposit) = 1200(1.015)^2 = 1236.27`

`text(Value of 3rd deposit) = 1200(1.015) = 1218`

`text(Value of 4th deposit) = 1200`
 

`:.\ text(Amount in account after 2 years)`

`= 1254.81 + 1236.27 + 1218 + 1200`

`=$4909.08`

`=> A`

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)

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`$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 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?

  1. `10\ 000 xx (1 + 0.03)^4`
  2. `10\ 000 xx (1 + 0.03)^48`
  3. `10\ 000 xx (1 + 0.03/12)^4`
  4. `10\ 000 xx (1 + 0.03/12)^48`
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`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 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)

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`$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?

  1. $8919
  2. $11 156
  3. $49 173
  4. $49 316
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`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 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)

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`$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 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?  

  1. `35\ 000(1 + 0.03)^25`
  2. `35\ 000(1 + 3)^25` 
  3. `35\ 000 xx 25 xx 0.03`
  4. `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`