Compound Interest (OCR GCSE Maths) : Revision Note

Compound Interest

What is compound interest?

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

  • This is different from simple interest where interest is only based on 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

How do I calculate depreciation?

• A similar method can be used if something decreases in value by a percentage every year (e.g. a car)

• This is known as depreciation 

• Change the multiplier to one which represents a percentage decrease

  • e.g. a decrease of 15% would be a multiplier of 0.85

• If a car worth £ 16 000 depreciates by 15% each year for 6 years

  • Its value will be 16 000 × 0.85⁶, which is £ 6034.39

Compound interest formula

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

  • Final balance = where

    • P is the original amount,

    • r is the % increase,

    • and n is the number of years

  • Note that  is the same value as the multiplier

    • e.g. 1.15 for 15% interest

• This formula is not given in the exam