Question

A machine costing Rs.80,000 would reduce to Rs.20,000 in 8 years. Find the rate of yearly depreciation, given that the depreciation is calculated using diminishing balances method

Answer 1

Answer 2

Given:

• Initial cost (C₀) = Rs. 80,000

• Salvage value after 8 years (Cₙ) = Rs. 20,000

• Time (n) = 8 years

Formula for Diminishing Balance Depreciation:

$$C_n=C_0\times (1-r{)}^n$$

Where:

• $r$ = yearly depreciation rate (in decimal)

Step 1: Plug in the values

$$20,000=80,000\times (1-r{)}^8$$

Step 2: Simplify the equation

$$\frac{20,000}{80,000}=(1-r{)}^8$$$$0.25=(1-r{)}^8$$

Step 3: Solve for $(1-r)$
Take the 8th root of both sides:

$$1-r=0.25^{1\mathrm{/}8}$$$$1-r\approx 0.8409\text{(using a calculator)}$$

Step 4: Calculate $r$

$$r=1-0.8409=0.1591$$

Step 5: Convert to percentage

$$r\approx 15.91\mathrm{\%}$$

Final Answer:

The yearly depreciation rate is 15.91%.