Define repeated percentage change .

Repeated percentage change is when several percentage increases or decreases are applied to a quantity one after the other . Each change acts on the new amount produced by the change before it, not on the original amount.

Define compound interest .

Compound interest is interest added to an amount at regular intervals, with each new lot of interest worked out on the total so far rather than on the starting amount. It applies both to money saved , where it increases the amount saved, and to money owed , where it increases the debt.

True or False? With compound interest at 4% per year, more interest is added in the second year than in the first.

True. In the second year the 4% is worked out on the original amount plus the interest already added in the first year. That is what makes the interest compound : the amount added grows from one period to the next.

What tells you how many times to apply the change in a compound interest question?

The question states the time period for each change, which is often a year but may be a month or a week. Apply the change once for each of those periods that the money is invested or owed for.

Why can a loan with regular repayments not be worked out using a single multiplier?

A repayment subtracts a fixed amount of money, which is not a percentage change, so it cannot be folded into a multiplier. The amount owed has to be worked out step by step : add the interest, subtract the repayment, then repeat for the next period.

In a loan question, why does it matter whether the repayment is made before or after the interest is added?

Interest is charged on whatever is owed at that moment , so making the repayment first means the interest is worked out on a smaller amount. The two orders therefore give different answers, and the question always makes clear which one applies.

Define depreciation .

Depreciation is a repeated percentage decrease in the value of something over time. Cars, laptops and mobile phones are the usual examples, and the value normally falls by a percentage each year.

True or False? Depreciation questions are worked out using the same method as compound interest questions.

True. Both are repeated percentage change, and the only difference is that depreciation uses a multiplier less than 1 while compound interest uses one greater than 1 . So the method is the same either way: find the multiplier for one period, then apply it once for each period.

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Repeated Percentage Change (Edexcel IGCSE Maths B): Flashcards

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Define repeated percentage change.
Repeated percentage change is when several percentage increases or decreases are applied to a quantity one after the other.
Each change acts on the new amount produced by the change before it, not on the original amount.
An amount of $10000$ is increased by 10% three times in a row. Fill in the missing multiplier.
$10000 \times______^{3} = 13310$
The completed calculation is:
$10000 \times 1 . 1^{3} = 13310$
The multiplier for a 10% increase is $1.1$ , and repeating the same change three times means raising that multiplier to the power 3.
True or False?
Increasing an amount by 10% three times in a row is the same as increasing it by 30% once.
False.
Repeating a 10% increase three times multiplies by $1 . 1^{3} = 1.331$ , while a single 30% increase multiplies by $1.3$ .
Starting from $10000$ these give $13310$ and $13000$ , because each repeat acts on the larger amount left by the one before.
A population of $8000$ falls by 5% each year. How many times is the change applied between the start of 2025 and the start of 2028, and what is the population then?
The change is applied three times, once for each of the years 2025 to 2026, 2026 to 2027 and 2027 to 2028.
So the population is $8000 \times 0 . 95^{3} = 6859$ .
An amount is decreased by 14% and then decreased by 9%. How do you find the final amount?
Multiply the original amount by the multiplier for each change in turn, so multiply by $0.86$ and then by $0.91$ .
For an original amount of $10000$ this gives $10000 \times 0.86 \times 0.91 = 7826$ .
True or False?
Increasing an amount by 3.4% and then decreasing the result by 3.4% brings it back to the amount you started with.
False.
The multipliers are $1.034$ and $0.966$ , and $1.034 \times 0.966 = 0.998844$ , which is less than 1.
The decrease is taken from a larger amount than the increase was added to, so $250000$ becomes $249711$ rather than returning to $250000$ .
Define compound interest.
Compound interest is interest added to an amount at regular intervals, with each new lot of interest worked out on the total so far rather than on the starting amount.
It applies both to money saved, where it increases the amount saved, and to money owed, where it increases the debt.
True or False?
With compound interest at 4% per year, more interest is added in the second year than in the first.
True.
In the second year the 4% is worked out on the original amount plus the interest already added in the first year.
That is what makes the interest compound: the amount added grows from one period to the next.
What tells you how many times to apply the change in a compound interest question?
The question states the time period for each change, which is often a year but may be a month or a week.
Apply the change once for each of those periods that the money is invested or owed for.
Why can a loan with regular repayments not be worked out using a single multiplier?
A repayment subtracts a fixed amount of money, which is not a percentage change, so it cannot be folded into a multiplier.
The amount owed has to be worked out step by step: add the interest, subtract the repayment, then repeat for the next period.
A loan of 22000 dollars has 5% interest added, and then 5000 dollars is repaid. Fill in the missing multiplier.
$(22000 \times______) - 5000 = 18100$
The completed calculation is:
$(22000 \times 1.05) - 5000 = 18100$
The multiplier for a 5% increase is $1.05$ , and the repayment is subtracted afterwards rather than built into the multiplier.
In a loan question, why does it matter whether the repayment is made before or after the interest is added?
Interest is charged on whatever is owed at that moment, so making the repayment first means the interest is worked out on a smaller amount.
The two orders therefore give different answers, and the question always makes clear which one applies.
Define depreciation.
Depreciation is a repeated percentage decrease in the value of something over time.
Cars, laptops and mobile phones are the usual examples, and the value normally falls by a percentage each year.
What does it mean to say that a car depreciates by 15% a year?
Its value falls by 15% each year, and each year's 15% is taken from the value at the start of that year rather than from the original price.
So the value is multiplied by $0.85$ once for each year that passes.
A car costing $30000$ pounds depreciates by 12% in its first year and by 8% in each of the next two years. Fill in the two missing multipliers.
$30000 \times______\times______^{2} = 22344.96$
The completed calculation is:
$30000 \times 0.88 \times 0 . 92^{2} = 22344.96$
A rate that is repeated gets a power, while a rate used once is simply multiplied in, so the 8% decrease is squared and the 12% decrease is not.
True or False?
Depreciation questions are worked out using the same method as compound interest questions.
True.
Both are repeated percentage change, and the only difference is that depreciation uses a multiplier less than 1 while compound interest uses one greater than 1.
So the method is the same either way: find the multiplier for one period, then apply it once for each period.
If a value depreciates by 2% each month, what multiplier applies over one year?
The multiplier for one month is $0.98$ , and a year contains 12 months, so the multiplier for the whole year is $0 . 98^{12}$ .
That comes to about $0.785$ , so the value falls by roughly 21.5% over the year.

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