Answer :
Let's tackle this question step by step:
1. Initial Problem Understanding:
- The lathe originally costs £3000.
- It depreciates by 15% each year.
- We are to find its value after 4 years and determine when its value falls below £550.
2. Calculate Value After 4 Years:
- The depreciation formula to calculate the value after a certain number of years is:
[tex]\[
\text{Value after } n \text{ years} = \text{Initial value} \times (1 - \text{Depreciation rate})^n
\][/tex]
- Plug in the initial value (£3000), the depreciation rate (15% or 0.15), and the number of years (4):
[tex]\[
\text{Value after 4 years} = 3000 \times (1 - 0.15)^4
\][/tex]
- The calculated value of the lathe after 4 years is approximately £1566.02.
3. Determine When the Lathe Should Be Sold:
- We need to find out after how many years the value of the lathe drops below £550.
- Start from the initial value (£3000) and keep applying the 15% depreciation each year until the value is less than £550.
- Continue subtracting 15% year by year:
- Year 1: £3000 \times 0.85
- Year 2: Result from Year 1 \times 0.85
- Repeat until the result is less than £550.
- After calculating, the lathe reaches a value below £550 after 11 years.
So, the value of the lathe after 4 years is approximately £1566.02. The lathe is sold after 11 years when its value falls below £550.
1. Initial Problem Understanding:
- The lathe originally costs £3000.
- It depreciates by 15% each year.
- We are to find its value after 4 years and determine when its value falls below £550.
2. Calculate Value After 4 Years:
- The depreciation formula to calculate the value after a certain number of years is:
[tex]\[
\text{Value after } n \text{ years} = \text{Initial value} \times (1 - \text{Depreciation rate})^n
\][/tex]
- Plug in the initial value (£3000), the depreciation rate (15% or 0.15), and the number of years (4):
[tex]\[
\text{Value after 4 years} = 3000 \times (1 - 0.15)^4
\][/tex]
- The calculated value of the lathe after 4 years is approximately £1566.02.
3. Determine When the Lathe Should Be Sold:
- We need to find out after how many years the value of the lathe drops below £550.
- Start from the initial value (£3000) and keep applying the 15% depreciation each year until the value is less than £550.
- Continue subtracting 15% year by year:
- Year 1: £3000 \times 0.85
- Year 2: Result from Year 1 \times 0.85
- Repeat until the result is less than £550.
- After calculating, the lathe reaches a value below £550 after 11 years.
So, the value of the lathe after 4 years is approximately £1566.02. The lathe is sold after 11 years when its value falls below £550.
