Math / Numbers & Operations

QuestionA caravan was bought for $£ 20,000$ . It depreciated by $11 \%$ in the first year. It then depreciated by a further 6\% each year over the next two years. Calculate the value of the caravan three years after it was bought.

Studdy Solution

STEP 1

1. The initial value of the caravan is $£20,000$ .
2. The depreciation rate for the first year is $11\%$ .
3. The depreciation rate for the second and third years is $6\%$ each year.
4. We need to calculate the value of the caravan after three years.

STEP 2

1. Calculate the value after the first year of depreciation.
2. Calculate the value after the second year of depreciation.
3. Calculate the value after the third year of depreciation.

STEP 3

Calculate the depreciation for the first year.
$\text{Depreciation for the first year} = 0.11 \times 20,000 = 2,200$
Subtract the depreciation from the initial value:
$\text{Value after first year} = 20,000 - 2,200 = 17,800$

STEP 4

Calculate the depreciation for the second year.
$\text{Depreciation for the second year} = 0.06 \times 17,800 = 1,068$
Subtract the depreciation from the value after the first year:
$\text{Value after second year} = 17,800 - 1,068 = 16,732$

STEP 5

Calculate the depreciation for the third year.
$\text{Depreciation for the third year} = 0.06 \times 16,732 = 1,003.92$
Subtract the depreciation from the value after the second year:
$\text{Value after third year} = 16,732 - 1,003.92 = 15,728.08$
The value of the caravan three years after it was bought is:
$\boxed{£15,728.08}$

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