AQA · Mathematics · 8300
GCSE Maths: Percentages: compound interest
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Percentages: compound interest (Corbettmaths Video 236), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is compound interest?
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Interest that is calculated on both the original amount and the accumulated interest from previous periods.
If £4000 earns 5% compound interest per year for 2 years, what is the total amount?
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£4410. Calculate: £4000 × 1.05 × 1.05 = £4410.
What multiplier would you use to calculate a 5% increase?
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1.05. Add the percentage as a decimal to 1 (1 + 0.05 = 1.05).
What multiplier would you use to calculate a 5% decrease?
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0.95. Subtract the percentage as a decimal from 1 (1 - 0.05 = 0.95).
If a car worth £10000 depreciates by 5% each year for 2 years, what is its value?
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£9025. Calculate: £10000 × 0.95 × 0.95 = £9025.
To calculate compound interest over multiple years, raise the multiplier to the ?.
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power of the number of years
Why is Florence's interest on £200 at 5% for 2 years more than £20?
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Because compound interest earns interest on interest. Year 1 earns £10, but Year 2 earns 5% on £210, giving £10.50, totaling £20.50.
In the formula V = 48000 × 0.88^t, what does the value 0.88 represent?
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The multiplier for a 12% annual decrease in value (1 - 0.12 = 0.88).
In the formula V = 48000 × 0.88^t, what does 48000 represent?
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The initial value or cost of the boat when t = 0.
If a ball rises to 60% of its previous height after each bounce, starting at 2 m, what height does it reach after the first bounce?
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1.2 m. Calculate: 2 × 0.60 = 1.2 m.
If £2400 is invested at 4.25% compound interest per annum for 8 years, what is the calculation needed?
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£2400 × (1.0425)^8. Raise the multiplier 1.0425 to the power of 8 years.
What is the effect of depreciation on an asset's value?
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Depreciation decreases the value of an asset over time.
How do you calculate the value of an asset after one year if it depreciates by 25%?
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Multiply the current value by 0.75 (or multiply by 1 - 0.25).
In compound interest with varying rates, how is the final value calculated?
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Apply each year's interest rate sequentially to the balance from the previous year.
What mathematical process models radioactive decay over time?
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Compound (exponential) decay, where the mass decreases by a fixed percentage each time period.
What formula structure is used to calculate a quantity after n periods of compound percentage decrease?
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Final value = Initial value × (1 - rate)^n, where rate is expressed as a decimal.
When comparing two investment options with compound interest, what calculation should you perform?
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Calculate the final value for each option using their respective rates and time periods, then compare the results.
If you know the initial investment, final amount, and time period, how can you find the compound interest rate?
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Rearrange the compound interest formula: rate = (Final/Initial)^(1/n) - 1, where n is the number of periods.
What is the difference between simple interest and compound interest?
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Simple interest is calculated only on the original principal, while compound interest is calculated on the principal plus any accumulated interest from previous periods.
How do you calculate water remaining in a tank after it loses 5% per minute for multiple minutes?
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Multiply the initial amount by 0.95^n, where n is the number of minutes.
If you know the amount after 2 years with compound interest, how can you find the amount after 3 years?
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First find the interest rate from the 2-year data, then apply that rate for the third year, or multiply the 2-year amount by (1 + r) once more.
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