Ratio, proportion and rates of changeKS3 / GCSE

Compound interest over a fixed number of periods

Use percentage multipliers for repeated or successive changes.

  • The original amount is 100%. A increase 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

is invested at compound interest per year. Find its value after years, to the nearest penny.

The original amount is 100%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
The original amount is 100%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.

Example 2

is invested at compound interest per year. Find its value after years, to the nearest penny.

The original amount is 100%. Add 4%; 104% remains. is the multiplier: 104% is 1.04 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%. Add 4%; 104% remains. is the multiplier: 104% is 1.04 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

is invested at compound interest per year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Add 5%; 105% remains. is the multiplier: 105% is 1.05 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%. Add 5%; 105% remains. is the multiplier: 105% is 1.05 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 2

is invested at compound interest per year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Add 6%; 106% remains. is the multiplier: 106% is 1.06 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%. Add 6%; 106% remains. is the multiplier: 106% is 1.06 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

is invested at compound interest per year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Add 7%; 107% remains. is the multiplier: 107% is 1.07 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
The original amount is 100%. Add 7%; 107% remains. is the multiplier: 107% is 1.07 times the original amount.Apply the multiplier once for each year.Exact value, written to 2 decimal places.
Question 4

is invested at compound interest per year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Add 8%; 108% remains. is the multiplier: 108% is 1.08 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%. Add 8%; 108% remains. is the multiplier: 108% is 1.08 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

is invested at compound interest per year. Find its value after years, to the nearest penny.

Check answer
The original amount is 100%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 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%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 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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