Finding a repeated percentage rate
If A = P ×
- If A = P ×
to the power , divide A by P to find the overall multiplier. - Take the
th root to find the multiplier for one period. Use the calculator root or power key. - The percentage increase is (
) × 100; for a decrease it is ( ) × 100.
Example 1
An amount changes from £500 to £520.20 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
Example 2
An amount changes from £500 to £470.45 over 2 years at the same compound percentage rate each year. Find the annual percentage decrease.
Remember
Use the worked steps to check your method, not just the final answer.
Your turn
An amount changes from £500 to £540.80 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
Check answer
A multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £451.25 over 2 years at the same compound percentage rate each year. Find the annual percentage decrease.
Check answer
A multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £561.80 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
Check answer
A multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £432.45 over 2 years at the same compound percentage rate each year. Find the annual percentage decrease.
Check answer
A multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £583.20 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
Check answer
A multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £540.80 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
AnswerA multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £451.25 over 2 years at the same compound percentage rate each year. Find the annual percentage decrease.
AnswerA multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £561.80 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
AnswerA multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £432.45 over 2 years at the same compound percentage rate each year. Find the annual percentage decrease.
AnswerA multiplier below 1 is a decrease; above 1 is an increase.
An amount changes from £500 to £583.20 over 2 years at the same compound percentage rate each year. Find the annual percentage increase.
AnswerA multiplier below 1 is a decrease; above 1 is an increase.