Ratio, proportion and rates of changeKS3 / GCSE

Depreciation over a fixed number of periods

Use percentage multipliers for repeated or successive changes.

  • The original amount is 100%. A decrease leaves of the original amount.
  • is the multiplier: . Divide the percentage by 100 to write it as a decimal.
  • Use : is the initial amount, the multiplier for one year, the number of years and the final amount.
  • Keep the full value until the end. means more digits follow; round the final answer to the requested accuracy.

Example 1

A car worth loses of its value each year. Find its value after years, to the nearest penny.

The original amount is 100%. Subtract 8%; 92% remains. is the multiplier: 92% is 0.92 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
The original amount is 100%. Subtract 8%; 92% remains. is the multiplier: 92% is 0.92 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.

Example 2

A car worth loses of its value each year. Find its value after years, to the nearest penny.

The original amount is 100%. Subtract 9%; 91% remains. is the multiplier: 91% is 0.91 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
The original amount is 100%. Subtract 9%; 91% remains. is the multiplier: 91% is 0.91 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).

Your turn

Question 1

A car worth loses of its value each year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Subtract 10%; 90% remains. is the multiplier: 90% is 0.9 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
The original amount is 100%. Subtract 10%; 90% remains. is the multiplier: 90% is 0.9 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
Question 2

A car worth loses of its value each year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Subtract 11%; 89% remains. is the multiplier: 89% is 0.89 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
The original amount is 100%. Subtract 11%; 89% remains. is the multiplier: 89% is 0.89 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
Question 3

A car worth loses of its value each year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Subtract 12%; 88% remains. is the multiplier: 88% is 0.88 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
The original amount is 100%. Subtract 12%; 88% remains. is the multiplier: 88% is 0.88 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
Question 4

A car worth loses of its value each year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Subtract 13%; 87% remains. is the multiplier: 87% is 0.87 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
The original amount is 100%. Subtract 13%; 87% remains. is the multiplier: 87% is 0.87 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
Question 5

A car worth loses of its value each year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Subtract 14%; 86% remains. is the multiplier: 86% is 0.86 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
The original amount is 100%. Subtract 14%; 86% remains. is the multiplier: 86% is 0.86 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest penny (2 decimal places).
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