Tariq bought a new mazda for $18600. He wants to sell it in some years' time. Using the declining balance method of depreciation and a depreciation rate of 12% p.a., find how many years it will take for the car to be worth $7600

  7 years

Step-by-step explanation:

The depreciation rate of 12% using the declining balance method means the car is worth 12% less at the end of the year than it was worth at the beginning. That is, each year the value is multiplied by (1 -12%) = 0.88. So, after n years, the value has been multiplied by 0.88^n.

We want to find n such that ...

  7600 = 18600·0.88^n

  7600/18600 = 0.88^n

  log(76/186) = n·log(0.88)

  log(76/186)/log(0.88) = n ≈ 7.00

It will take 7 years for the value of the car to decline to $7600.

Comment on declining balance depreciation

Often, you will see declining balance depreciation specified in terms of an acceleration factor (often 150% or 200% ("double declining balance")) and a useful life. As with any depreciation, what is depreciated is the difference between the initial value and the salvage value. The percentage rate quoted above is essentially calculated as ...

  (acceleration factor)/(useful life) = depreciation rate per year

One way to get a 12% depreciation rate is using an acceleration factor of 150% and a useful life of 12.5 years (with a salvage value of 0).