Certainly! Let's solve this step-by-step.
Firstly, let's understand each part of the problem:
1. Initial value of the car: Mavis bought the car for R280,000.
2. Depreciation rate: The car depreciates at 18% per annum.
3. Time period: We need to find the value of the car after 3 years.
### Step-by-Step Solution:
1. Calculate the annual depreciation:
To find the annual depreciation, we use the formula:
[tex]\[
\text{Annual Depreciation} = \text{Initial Value} \times \text{Depreciation Rate}
\][/tex]
Given the initial value of R280,000 and the depreciation rate of 18% (which is 0.18 in decimal form):
[tex]\[
\text{Annual Depreciation} = 280,000 \times 0.18 = R50,400
\][/tex]
2. Calculate the total depreciation over 3 years:
Since the straight-line method is used, the depreciation is uniform every year. So, we can calculate the total depreciation over 3 years by multiplying the annual depreciation by the number of years:
[tex]\[
\text{Total Depreciation over 3 years} = \text{Annual Depreciation} \times \text{Number of Years}
\][/tex]
Thus,
[tex]\[
\text{Total Depreciation over 3 years} = 50,400 \times 3 = R151,200
\][/tex]
3. Calculate the value of the car after 3 years:
To determine the value of the car after 3 years, subtract the total depreciation from the initial value of the car:
[tex]\[
\text{Value after 3 years} = \text{Initial Value} - \text{Total Depreciation}
\][/tex]
Therefore,
[tex]\[
\text{Value after 3 years} = 280,000 - 151,200 = R128,800
\][/tex]
### Summary:
- Annual Depreciation: R50,400
- Total Depreciation over 3 years: R151,200
- Value of the car after 3 years: R128,800
Hence, the value of Mavis’s car after 3 years will be R128,800.
