SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

CORE, FUR1 2021 VCAA 18-19 MC

Deepa invests $500 000 in an annuity that provides an annual payment of $44 970.55

Interest is calculated annually.

The first five lines of the amortisation table are shown below.
 

Part 1

The principal reduction associated with payment number 3 is

  1. $17 962.40
  2. $25 969.37
  3. $27 008.15
  4. $28 088.47
  5. $44 970.55

 

Part 2

The number of years, in total, for which Deepa will receive the regular payment of `$44\ 970.55` is closest to

  1. 12
  2. 15
  3. 16
  4. 18
  5. 20
Show Answers Only

`text(Part 1:)\ C`

`text(Part 2:)\ B`

Show Worked Solution

`text{Part 1}`

`text{Principal reduction}` `= 449\ 060.08 – 422\ 051.93`
  `= 27\ 008.15`

`=> C`
 

`text{Part 2}`

♦ Mean mark part (2) 44%.

`text{Interest rate} = {20\ 000}/{500\ 000} = 4text{% p.a.}`
 

`text{Find}\ N\ text{by TVM solver:}`

`N` `= ?`
`I(%)` `= 4`
`PV` `= -500\ 000`
`PMT` `= 44\ 970.55`
`FV` `= 0`
`text(P/Y)` `= text(C/Y) = 1`

 
`:. N = 15.000`

`=> B`

CORE, FUR1 2017 VCAA 23 MC

Four lines of an amortisation table for an annuity investment are shown below.

The interest rate for this investment remains constant, but the payment value may vary.
 

     
 

The balance of the investment after payment number 20 is $7500.

The value of payment number 20 is closest to

  1.   `$29`
  2. `$100`
  3. `$135`
  4. `$237`
  5. `$295`
Show Answers Only

`D`

Show Worked Solution

`text(Principal addition)`

`= 7500 – 7233.83`

`= $266.17`

 

`text(From the table,)`

`text{Interest applicable (expected) ≈ $29}`

`:.\ text(Payment)` `~~ 266.17 – 29`
  `~~ $237.17`

`=> D`