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CORE, FUR1 2020 VCAA 25 MC

The graph below represents the value of an annuity investment, `A_n`, in dollars, after `n` time periods.
 


 

A recurrence relation that could match this graphical representation is

  1. `A_0 = 200\ 000, qquad A_(n+1) = 1.015A_n - 2500`
  2. `A_0 = 200\ 000, qquad A_(n+1) = 1.025A_n - 5000`
  3. `A_0 = 200\ 000, qquad A_(n+1) = 1.03A_n - 5500`
  4. `A_0 = 200\ 000, qquad A_(n+1) = 1.04A_n - 6000`
  5. `A_0 = 200\ 000, qquad A_(n+1) = 1.05A_n - 8000`
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`B`

Show Worked Solution

`text(The value doesn’t change.)`

`text(Consider option B:)`

`A_1` `= 1.025 xx 200\ 000 – 5000`
  `= 200\ 000`
  `= A_0`

 
`=>  B`

CORE, FUR1 SM-Bank 3 MC

The decreasing value of a depreciating asset is shown in the graph below.
 

 
 

Let `A_n` be the value of the asset after `n` years, in dollars.

What recurrence relation below models the value of `A_n`?

  1. `A_0 = 120\ 000,qquadA_n = 120\ 000 xx 1.125 xx n` 
  2. `A_0 = 120\ 000,qquadA_n = 120\ 000 xx (0.125)^n` 
  3. `A_0 = 120\ 000,qquadA_n = 120\ 000 xx (1 - 0.125) xx n` 
  4. `A_0 = 120\ 000,qquadA_n = 120\ 000 xx (1 - 0.125)^n` 
  5. `A_0 = 120\ 000,qquadA_n = 120\ 000 xx (1 + 1.125)^n` 
Show Answers Only

`D`

Show Worked Solution

`text(The asset is decreasing at 12.5% per year)`

`text(on a decreasing balance basis.)`

`A_1` `= 120\ 000(1 – 0.125)^1`
`vdots`  
`A_n` `= 120\ 000(1 – 0.125)^n`

`=> D`