Question 9
A new car costs $42 000. Its value depreciates by 15% each year using the diminishing-value method.
What is the car’s value at the end of 4 years?
Not quite. You used straight-line depreciation of 15% of the cost ($6300) each year: $42\,000 - 4 \times 6300 = 16\,800$.
Not quite. You gave the total depreciation instead of the value: $42\,000 - 21\,924.26 = 20\,075.74 \approx 20\,076$.
That is it. Step through the hints below to see why.
Not quite. You used $t_4$ (only 3 years of depreciation): $42\,000 \times 0.85^{3} = 25\,793.25 \approx 25\,793$.
| End of year | Value in dollars | Option |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
Diminishing value at 15% a year. The rows an option matches are in bold and named in the last column.
Choose an option to fill in the year by year values and see what the option matches.
Straight line takes 15% of the cost, $6300, every year: $42\,000 - 6300 \times 4 = 16\,800$. No year in the diminishing-value table has this value.
The drop from $42 000 to $21 924.26 is $42\,000 - 21\,924.26 = 20\,075.74$.
The year 4 value is $42\,000 \times 0.85^{4} = 21\,924.26$.
The year 3 value is $42\,000 \times 0.85^{3} = 25\,793.25$.
(A) uses straight-line depreciation, but this car depreciates by the diminishing-value method.
(B) is the amount the car lost over the 4 years, not what it is worth.
(C) is the value after 4 factors of 0.85, the end of 4 years.
(D) is the value after only 3 years of depreciation.
Try the question first. Choose a hint above when you want one.
$t_n = t_1 r^{n-1}$ with $t_1 = 42\,000$ (new), $r = 1 - 0.15 = 0.85$, and the end of 4 years is $t_5$.
$t_5 = 42\,000 \times 0.85^{4} = 21\,924.26$, so the car is worth $21 924.26 ($21 924).
Each year multiplies the value by 0.85, so 4 years of depreciation means 4 factors of 0.85.
With $r = 0.85$, the value at the end of 4 years is $t_5 = 42\,000 \times 0.85^{4} = 21\,924.26$, so the car is worth $21 924.
Only mark this done when you could do it without help. Reading the solution does not count.
A Tangent Tuition mock exam question. It is not a past QCAA question, and Tangent Tuition is not affiliated with the QCAA.
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