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Compound Interest

Maths: Edexcel IGCSE Higher, topic 1.6.4

Compound Growth and Decay

Growth and decay

Growth and decay

  • When an amount increases or decreases by a set percentage on a regular basis this is called compound growth or compound decay.
  • The amount that is lost/gained changes with each interval since the amount lost/gained is a percentage of the current amount.
Formula

Formula

  • This formula gives the amount after n intervals:
  • N = S × (multiplier)n
  • Where S is the starting amount and the multiplier is the percentage multiplier:
  • 1.25 for a 25% increase or 0.6 for a 40% decrease.

Compound Interest

In summer, the number of ants in a colony increases by 20% each day. On the first day there are 10,000 ants. How many are there after 3 days?

Key terms

Key terms

  • Compound interest is when the amount of interest for a bank account is calculated again each interval rather than just using the starting amount.
  • Depreciation is when the value of an item decreases each year as it ages.
Start with 10 000 ants

Start with 10 000 ants

Multiply by 1.2 because we want an increase of 20%

Multiply by 1.2 because we want an increase of 20%

Do the same again

Do the same again

And again for the 3rd day

And again for the 3rd day

  • We can also solve these problems using the formula:
  • N = S × (multiplier)n

Compound Interest

In summer, the number of ants in a colony increases by 20% each day. On the first day there are 10,000 ants. How many days until the colony numbers more than 30,000?

The formula for compound interest

The formula for compound interest

  • N is the number of ants
  • n is the number of days passed
On the 5th day there are 24 883 ants (to nearest whole number)

On the 5th day there are 24 883 ants (to nearest whole number)

On the 6th day there are 28 860 ants

On the 6th day there are 28 860 ants

On the 7th day there are 35 832 ants

On the 7th day there are 35 832 ants

Answer

Answer

  • This is the first day we are over 30 000 so the answer is 7 days.

Test yourself on Compound Interest

  • What's the formula for compound growth and decay?

  • What do we call it when an amount increases by a set percentage on a regular basis?

  • What do we call it when the value of an item decreases each year as it ages?

  • What do we call it when the amount of interest for a bank account is calculated again each interval rather than just using the starting amount?

  • If a company has 10 employees and every year the amount of employees increases by 10%, what's the formula for the amount of employees after 5 years?

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