Finding how many periods a target takes Revision Card

AI generatedRatio, proportion and rates of changeKS3 / GCSE

Make the percentage multiplier from () ÷ 100 or () ÷ 100.

Make the percentage multiplier from () ÷ 100 or () ÷ 100.
Start at period 0 and repeatedly multiply, keeping the calculator value unrounded.
Find the first whole period that meets the target. Check that the preceding period does not meet it.

Example 1

£200 earns 5% compound interest each year. What is the first whole number of years when the balance is at least £226?

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

Example 2

£210 earns 6% compound interest each year. What is the first whole number of years when the balance is at least £257?

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

£220 earns 7% compound interest each year. What is the first whole number of years when the balance is at least £298?

Check answer

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

At year 4 the balance is below £298; at year 5 it is above the target.

Question 2

£230 earns 8% compound interest each year. What is the first whole number of years when the balance is at least £279?

Check answer

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

At year 2 the balance is below £279; at year 3 it is above the target.

Question 3

£240 earns 9% compound interest each year. What is the first whole number of years when the balance is at least £324?

Check answer

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

At year 3 the balance is below £324; at year 4 it is above the target.

Question 4

£250 earns 10% compound interest each year. What is the first whole number of years when the balance is at least £384?

Check answer

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

At year 4 the balance is below £384; at year 5 it is above the target.

Question 5

£260 earns 5% compound interest each year. What is the first whole number of years when the balance is at least £293?

Check answer

The starting amount is 100%.

Convert the new percentage to a fraction of 100.

This is the multiplier for one period.

Before any interest is added.

Retain the full calculator value.

At year 2 the balance is below £293; at year 3 it is above the target.