Which calculation gives the value of $300 after 4 years at 3% compound interest?

300 × 1.03⁴. The multiplier 1.03 is applied four times.

How does compound interest differ from simple interest?

Interest is also earned on the interest already added. That is why the amount grows faster each year.

Compound interest, growth and decay · Cambridge IGCSE Mathematics

In plain words

With compound interest you earn interest on your interest, so the amount grows faster every year. The same idea, a fixed percentage change repeated again and again, describes a car losing value, a population growing, and bacteria multiplying.

Three things to know

Compound interest: amount = P × (1 + r/100)ⁿ, where P is the starting amount, r the percentage rate and n the number of years.
For something losing value (depreciation), the multiplier is less than 1: a 10% fall each year is × 0.9 each year.
Exponential growth means multiplying by the same number in each equal period of time.

Worked example

$2000 is invested at 5% per year compound interest. Find its value after 3 years.

The multiplier for a 5% increase is 1.05.
After 3 years: 2000 × 1.05³.
= $2315.25.

Tips and tricks

Use a power, not three separate steps: it is quicker and there is less to go wrong.
"How much interest?" means take the starting amount off at the end.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Compound interest, growth and decay: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Which calculation gives the value of $300 after 4 years at 3% compound interest?
- 300 × 1.03 × 4
- 300 × 0.03⁴
- 300 × 1.03⁴ (the answer)
- 300 × 1.12
The multiplier 1.03 is applied four times.
$100 is invested at 10% per year compound interest. What is it worth after 2 years?
- $110
- $120
- $121 (the answer)
- $200
100 × 1.1 × 1.1.
A phone worth $1000 loses 20% of its value each year. What is it worth after 2 years?
- $600
- $640 (the answer)
- $800
- $960
1000 × 0.8 × 0.8.
How does compound interest differ from simple interest?
- It is always a lower rate.
- Interest is also earned on the interest already added. (the answer)
- It is paid only once.
- There is no difference.
That is why the amount grows faster each year.
A colony of 10 bacteria triples every hour. How many are there after 3 hours?
- 30
- 90
- 270 (the answer)
- 1000
10 × 3³.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.