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Financial Maths, GEN1 2024 NHT 24 MC

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.

This amount was closest to

  1. $ 224.03
  2. $ 225.97
  3. $ 228.62
  4. $ 229.38
  5. $ 231.46
Show Answers Only

\(A\)

Show Worked Solution

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

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

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

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

\(V \times 1.08 = 19\,288.80\ \ \Rightarrow\ \ V=17\,860\)

\(\therefore \ \text{Extra payment}\ = 17\,860-17\,635.97=$224.03 \)

\(\Rightarrow A\)

CORE, FUR1 2019 VCAA 21 MC

The graph below shows the value, in dollars, of a compound interest investment after `n` compounding periods, `V_n`, for a period of four compounding periods.
 


 

The coordinates of the point where  `n = 2`  are  `(2, b)`.

The value of  `b`  is

  1. 660.00
  2. 670.00
  3. 672.80
  4. 678.40
  5. 685.60
Show Answers Only

`C`

Show Worked Solution

`text(Let)\ \ r = text(rate of interest)`

`V_0` `= 500`
`V_1` `= V_0 xx (1 + r)^n`
`580` `= 500 (1 + r)^1`
`1 + r` `= 1.16`
`r` `= 16text(%)`

 

`:. b` `= 500 (1.16)^2`
  `= 672.80`

 
`=>  C`

CORE*, FUR2 2010 VCAA 3

Simple Saver is a simple interest investment in which interest is paid annually.

Growth Plus is a compound interest investment in which interest is paid annually.

Initially, $8000 is invested with both Simple Saver and Growth Plus.

The graph below shows the total value (principal and all interest earned) of each of these investments over a 15 year period.

The increase in the value of each investment over time is due to interest
 

BUSINESS, FUR2 2010 VCAA 3
 

  1. Which investment pays the highest annual interest rate, Growth Plus or Simple Saver?

     

    Give a reason to justify your answer.   (1 mark)

  2. After 15 years, the total value (principal and all interest earned) of the Simple Saver investment is $21 800.

     

    Find the amount of interest paid annually.   (1 mark)

  3. After 15 years, the total value (principal and all interest earned) of the Growth Plus investment is $24 000.

     

    1. Write down an equation that can be used to find the annual compound interest rate, `r`.   (1 mark)

    2. Determine the annual compound interest rate.

       

      Write your answer as a percentage correct to one decimal place.   (1 mark)

Show Answers Only
  1. `text(Simple Saver has the highest annual)`
    `text(interest rate because after 1 year,)`
    `text(the value of investment is higher.)`
  2. `$920`
    1. `24\ 000 = 8000 (1 + r/100)^15`
    2. `7.6text{%  (1 d.p.)}`
Show Worked Solution

a.   `text(Simple Saver has the highest annual)`

♦♦♦ Part (a) was “very” poorly answered although exact data unavailable.
MARKER’S COMMENT: Most students ignored the word “rate” and instead referred to the eventual return of each investment.

`text(interest rate because after 1 year,)`

`text(the value of investment is higher.)`
  

b.   `text(Total interest earned)`

`= 21\ 800-8000`

`= $13\ 800`

`:.\ text(Interest paid annually)`

`= (13\ 800)/15`

`= $920`
  

c.i.   `text(Using)\ A = PR^n,`

`24\ 000 = 8000 (1 + r/100)^15`
  

c.ii.    `(1 + r/100)^15` `= 3`
  `1 + r/100` `= 1.0759…`
  `:. r` `= 0.0759…`
    `= 7.6text{%  (1 d.p.)}`

CORE*, FUR1 2006 VCAA 8 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?

A.   interest is compounding annually and is credited annually

B.   interest is compounding annually and is credited quarterly

C.   interest is compounding quarterly and is credited quarterly

D.   simple interest is paid on the opening balance and is credited annually

E.   simple interest is paid on the opening balance and is credited quarterly

Show Answers Only

`A`

Show Worked Solution

`text(From the graph, as balance increases after)`

♦ Mean mark 37%.
MARKERS’ COMMENT: Graphical analysis of financial situations is a requirement of the study design and deserves attention.

`text(each year, interest is credited annually.)`

`:.\ text(Eliminate)\ B, C\ text(and)\ E.`

`text(The difference of the balances between successive)`

`text(years is increasing which indicates that interest is)`

`text(compounding.)`

`:.\ text(Eliminate)\ D.`

`=>  A`