Compound Interest (Edexcel IGCSE Maths A) : Revision Note

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Compound Interest

What is compound interest?

  • Compound interest is where interest is calculated on the running total, not just the starting amount

  • E.g. $ 100 earns 10% interest each year, for 3 years

    • At the end of year 1, 10% of $ 100 is earned

      • The total balance will now be 100+10 = $ 110

    • At the end of year 2, 10% of $ 110 is earned

      • The balance will now be 110+11 = $ 121

    • At the end of year 3, 10% of $ 121 is earned

      • The balance will now be 121+12.1 = $ 133.10

How do I calculate compound interest?

  • Compound interest increases an amount by a percentage and then increases the new amount by the same percentage

    • This process repeats each time period (yearly or monthly etc)

  • We can use a multiplier to carry out the percentage increase multiple times

    • To increase $ 300 by 5% once, we would find 300×1.05

    • To increase $ 300 by 5%, each year for 2 years, we would find (300×1.05)×1.05

      • This could be rewritten as 300×1.052

    • To increase $ 300 by 5%, each year for 3 years, we would find ((300×1.05)×1.05)×1.05

      • This could be rewritten as 300×1.053

  • This can be extended to any number of periods that the interest is applied for 

    • If $ 2000 is subject to 4% compound interest each year for 12 years

    • Find 2000×1.0412, which is $ 3202.06

  • Note that this method calculates the total balance at the end of the period, not the interest earned

Compound interest formula

  • An alternative method is to use the following formula to calculate the final balance

    • Final balance = P open parentheses 1 plus r over 100 close parentheses to the power of n space end exponent where

      • P is the original amount,

      • r is the % increase,

      • and n is the number of years

    • Note that 1 plus r over 100 is the same value as the multiplier

      • e.g. 1.15 for 15% interest

  • This formula is not given in the exam

How do I solve reverse compound interest problems?

  • You could be told the final balance after compound interest has been applied, and need to find the original amount

    • This could be referred to as a "reverse compound interest" problem

  • For example if:

    • The final balance is £432

    • After 20% interest has been applied each year

    • For 3 years

  • Using the same method as above, this can be written as an equation:

    • 432 equals P cross times 1.20 cubed where P is the original amount

    • Solve for P,

      • Divide both sides by 1.20 cubed

      • table row cell 432 divided by 1.20 cubed end cell equals P end table

      • P equals £ 250

  • In general, to find the original amount:

    • Divide the final amount by m to the power of n where

      • m is the multiplier for the time period

      • and n is the number of time periods (usually years)

Examiner Tips and Tricks

  • The formula for compound interest is not given in the exam

Worked Example

Jasmina 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?

Method 1

We want an increase of 4% per year
This is equivalent to a multiplier of 1.04, or 104% of the original amount

This multiplier is applied 7 timescross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 space equals space 1.04 to the power of 7

Therefore the final value after 7 years will be

1200 cross times 1.04 to the power of 7 equals $ 1579.118135...

Round to the nearest dollar

bold $ bold 1579

Method 2
Using the formula for the final amount   P open parentheses 1 plus r over 100 close parentheses to the power of n space end exponent
Substitute P is 1200, r = 4 and n = 7 into the formula 

1200 open parentheses 1 plus 4 over 100 close parentheses to the power of 7

bold $ bold 1579

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Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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