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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.)}`

Compound Interest, SMB-022 MC

The points on the graph below show the balance of an investment at the start of each quarter for a period of six years.

The same rate of interest applied for these six years.
 

   

In relation to this investment, which one of the following statements is true?

  1. interest is compounding annually and is credited annually
  2. interest is compounding annually and is credited quarterly
  3. simple interest is paid on the opening balance and is credited annually
  4. simple interest is paid on the opening balance and is credited quarterly
Show Answers Only

`A`

Show Worked Solution

`text{By elimination:}`

`text{From the graph, as balance increases after each year, interest is}`

`text{credited annually (eliminate B and D).}`

`text{The difference of the balances between successive years is increasing}`

`text{which indicates that interest is compounding (eliminate D).}`

`=>  A`

Compound Interest, SMB-014

Sam and Charlie each invest $5000 for three years.

Sam’s investment earns simple interest at the rate of 7.5% per annum.

Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.

At the conclusion of three years, determine which investment has the highest value and by how much.   (4 marks)

Show Answers Only

 `text{Charlie’s investment is worth $86.48 more than Sam’s.}`

Show Worked Solution

`text(Sam’s Investment:)`

`I=Prn = 5000 xx \frac{7.5}{100} xx 3 = $1125`

`text{Investment value}\ = 5000 + 1125 = $6125`

  
`text(Charlie’s Investment:)`

`FV` `= PV(1+r)^n`
  `= 5000 xx 1.075^3`
  `= $6211.48`

 
`text{Difference}\ = 6211.48-6125= $86.48`

`:.\ \text{Charlie’s investment is worth $86.48 more than Sam’s.}`

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.

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

  2. 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)

Show Answers Only
  1. `$37\ 158.72`
  2. `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.)}`