What is the depreciation rate? (Depreciation is calculated on the reducing balance.)

Question

ScanSolve AI Tutor · Accepted Answer

To find the depreciation rate using the reducing balance method, we use the formula:

S = P(1 - r)^n

where $S$ is the selling price, $P$ is the original purchase price, $r$ is the depreciation rate, and $n$ is the number of years.

Identify the given values.
The original purchase price $P = \text{R}250\,000$ .
The selling price after 4 years $S = \text{R}100\,000$ .
The number of years $n = 4$ .
Substitute the values into the formula.
$\text{R}100\,000 = \text{R}250\,000(1 - r)^4$
Isolate the term $(1 - r)^4$ .
$\frac{100\,000}{250\,000} = (1 - r)^4$ $0.4 = (1 - r)^4$
Solve for $(1 - r)$ by taking the fourth root of both sides.
$1 - r = (0.4)^{\frac{1}{4}}$ $1 - r \approx 0.7952719$
Solve for $r$ .
$r = 1 - 0.7952719$ $r \approx 0.2047281$
Convert the rate to a percentage.
$r \approx 0.2047281 \times 100\%$ $r \approx \textbf{20.47\%}$
The depreciation rate is $\boxed{\text{20.47\%}}$ .

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