Compund Interest
Maths: Edexcel A Level Pure Maths, topic 6.2.6
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
- 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 6th day there are 28 860 ants
On the 7th day there are 35 832 ants
Answer
- This is the first day we are over 30 000 so the answer is 7 days.
Number of ants per hour
- By using the rule for raising a power to another power, we can convert the multiplier for the growth after days into one that shows the growth every hour
- This way we see that there is a 0.8% increase in the number of ants every hour.
Test yourself on Compund Interest
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?
If a company has 150 employees and every year the amount of employees increases by 5%, what's the formula for the amount of employees after 20 years?
If a company has 12 employees and every year the amount of employees increases by 20%, what's the formula for the amount of employees after 2 years?