Question

A new motor bike is valued at shs 200000. Its value is known to depreciate at a constant rate per annum. Its value after 5 years is shs 80000. Calculate the rate of depreciation per annum and How long will it take for its value to be kshs 60000.pls explain in a simple way so that i can understand please.

Answer 1

To calculate the rate of depreciation of the motorbike, we can use the formula for depreciation over time. The straight-line depreciation formula can be expressed as:

\[ V = P - (d \times t) \]

Where:

• \(V\) is the value after time \(t\),
• \(P\) is the initial value (or purchase price),
• \(d\) is the annual depreciation,
• \(t\) is the time in years.

Step 1: Calculate the Annual Depreciation

1. Initial Value (P): 200,000 shs
2. Value after 5 years (V): 80,000 shs
3. Time (t): 5 years

Using the formula:

\[ V = P - (d \times t) \]

We can rearrange it to solve for \(d\):

\[ d = \frac{P - V}{t} \]

Substituting the known values into the equation:

\[ d = \frac{200000 - 80000}{5} \]

\[ d = \frac{120000}{5} = 24000 \text{ shs per year} \]

Step 2: Calculate the Rate of Depreciation (%)

To find the rate of depreciation per annum, we divide the annual depreciation by the initial value and multiply by 100 to get it in percentage:

\[ \text{Rate of Depreciation} = \left( \frac{d}{P} \right) \times 100 \]

Substituting in the values we know:

\[ \text{Rate of Depreciation} = \left( \frac{24000}{200000} \right) \times 100 \]

\[ \text{Rate of Depreciation} = 0.12 \times 100 = 12% \]

Conclusion of Step 1

So, the annual rate of depreciation is 12% per annum.

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Step 3: How Long Will it Take for its Value to be 60,000 Shs?

We want to find out how many years (let's call it \(t\)) it will take for the bike’s value to decrease from 200,000 shs to 60,000 shs.

Using the depreciation formula again:

\[ V = P - (d \times t) \]

Where:

• \(V\) is 60,000 shs,
• \(P\) is 200,000 shs,
• \(d\) is 24,000 shs/year (as calculated),
• We need to solve for \(t\).

Rearranging for \(t\):

\[ t = \frac{P - V}{d} \]

Substituting the known values:

\[ t = \frac{200000 - 60000}{24000} \]

\[ t = \frac{140000}{24000} \approx 5.83 \text{ years} \]

Conclusion of Step 3

It will take approximately 5.83 years for the value of the motorbike to depreciate to 60,000 shs.

Summary

• The rate of depreciation of the motorbike is 12% per annum.
• It will take about 5.83 years for its value to drop to 60,000 shs.