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Financial Maths - declining balance depreciation.
Test Yourself 1 - Solutions.


 

Future value. 1. Value = $999×(1 - 25%)3 = $421.45.

So value is $420 (to the nearest $10) after 3 years?
 

2. Value = $3200 × (1 - 20%)4 = $1,310.72.

So value is $1,310 (to the nearest $10) after 4 years?
 

3. Value = $132000 × (1 - 22.5%)5 = $36,904.76.
 

4. (a) is a straight line graph and so is a constant amount of decline each year.

(b) is like the quadrant of a circle and it starts off with a small % change which increases. So not a constant % decline as is needed.

(c) is an negative exponential curve as required for a declining balance situation but the cuve does not start at t = 0 - that is at the original value on the vertical axis.

(d) is the correct graph as it is negative exponential in shape and begins at $12,000 when t = 0.
 

5. Purchase price: $15,000.

Salvage value = 15000 × (1 - 10%)8 = $6,457.
Present value. 6.
  7.
  8.
  9.
  10.
Rate of depreciation. 11.
 

12. (i) The equipment reduces in value from $43,600 to $36,188. As a percentage this reduction is

(ii)

 

13. (i)

(ii)

(iii) The boat was valued at $38,000 when David first saw it. Hence we are going back 4 years before the boat had reached that level.
Number of periods -
Hint: use guess and check.

14. A PS4 console was purchased for $1400 a number of years ago. It is now valued at $400 after depreciating at a declining balance rate of 23% per year.

Approximately how many years ago was the PS4 purchased?

Answer. Purchased about 5 years ago.
  15.