Compound Interest (Edexcel IGCSE Maths)
Spec point —
1C
Compound interest
What is compound interest?
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Compound interest is a type of repeated percentage change
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Interest is money that is regularly added to an original amount of money
- This could be added yearly, monthly, etc.
- When saving money, interest increases the amount saved
- With debt, interest increases the amount owed
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With compound interest the amount added increases from period to period
- This is because in the second period interest is earned on the original amount and on the interest added in the first period
- And in the third period interest is earned on the original amount, the interest added in the first period, and the interest added in the second period
- Etc.
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The time period for each change is often a year
- Changes may also occur monthly, weekly, etc.
- An exam question will specify what the time period is
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The rate of percentage increase may be constant, or may vary from period to period
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Compound interest questions are answered using the usual techniques for repeated percentage change
- Be sure to answer in the context of the question
Worked Example Mary invests $1200 in a savings account, which pays compound interest at the rate of 4% per year for 7 years.
To the nearest dollar, what is her investment worth at the end of the 7 years?
Answer:
4% compound interest per year means a repeated percentage increase of 4% per year
The multiplier for a 4% increase is 1.04
The increase occurs 7 times (for the seven years)
- So multiply $1200 by
1200×1.04^7=$ 1579.118135...Round to the nearest dollar
Final answer:
bold $ bold 1579(to the nearest dollar)
Compound interest and loan repayments
Spec point —
1C
Compound interest & loan repayments
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In compound interest questions involving loans, part of the loan may also be repaid during each period
- This may occur before or after the interest is calculated
- Read the question carefully
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In this type of question, there is no 'shortcut' to the answer
- E.g. by multiplying the original amount one time by a percentage multiplier raised to a power
- You will need to work out the answer step by step
Worked Example David borrowed some money from Seren.
He borrowed $22 000 on 1st January 2024.
On 31st December each year, starting on 31st December 2024, Seren charged David interest of 5% on the amount of money that he owed her. This interest was added to the amount of money that David owed Seren.
On 1st January each year, starting on 1st January 2025, David repaid $5000 to Seren.
(a) Show that before David had repaid $5000 to Seren on 1st January 2025, he owed Seren $23 100.
Answer:
On 31st December 2024, 5% was added to the amount David owed Seren
At that point he still owed her the original $22 000
- So multiply $22 000 by 1.05 to increase it by 5%
Final answer: Before repaying Seren on 1st January 2025, David owed Seren $23 100
(b) After David had repaid $5000 to Seren on 1st January 2026, calculate how much money David now owed Seren.
Answer:
You need to work this out in steps
After adding the 31st December 2024 interest, David owed Seren $23 100
- But then on 1st January 2025 he repaid $5000
After the 1st January 2025 repayment, David owed Seren
23100 minus 5000 equals $ 18100Then on 31st December 2025, 5% interest was added on the remaining amount
- Multiply $18 100 by 1.05
After the interest added on 31st December 2025, David owed Seren
18100×1.05=$ 19005And finally, on 1st January 2026 David repaid Seren another $5000
After the 1st January 2026 repayment, David owed Seren
19005 minus 5000 equals $ 14005Final answer: $14 005
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