Ratio

Percentage change

Compare repeated growth with a fixed change.

Predict, test and explain

Step 1 of 3

Predict

£100 grows by 10% per period. What is it after two periods?

An=100(1+10100)6A_n=100\left(1+\frac{10}{100}\right)^{6}
00
22
44
66
88
1010
1212
00
4949
9797
146146
195195
period\text{period}
amount\text{amount}

Scroll the diagram sideways to see every label.

Percentage each periodA6≈177.16A_{6}\approx 177.16Fixed change100+6×(10)=160100+6\times(10)=160

Blue: each percentage applies to the latest amount. Red: add or subtract the same amount every period. A fixed decrease can cross zero.

InvestigateWhy does repeated percentage growth curve upwards?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

£80 increases by 10% each year. What is the amount after two years?

Hint

Apply the multiplier 1.10 twice.

Reveal answer

£96.80. The second increase applies to £88, the new amount.

80×1.102=96.8080\times1.10^2=96.80

Build an explanation

Hint 1

Turn the percentage change into a multiplier.

Hint 2

Each period's percentage applies to the current amount.

Hint 3

After n periods, use starting amount × (1 + rate/100)ⁿ; a decrease uses a multiplier below 1.

Worked example

This example uses fixed values, separate from the diagram controls.

An amount of 100 grows by 10% per period. Find it after two periods.

  1. The multiplier is 1 + 10/100 = 1.1.
  2. After one period: 100 × 1.1 = 110.
  3. After two: 110 × 1.1 = 121.

Answer: 121, compared with 120 for a fixed increase of 10 per period.

Connect this idea

Watch out: Repeated percentage growth uses a changing base, so it is not a fixed amount added each period.