Simple and compound interest: IB MYP 3 Mathematics Notes

What Is Interest?

Interest: Interest is the extra money earned (or owed) on an amount of money over time. It is usually expressed as a percentage of the original amount.

When you put money in a bank or invest it somewhere, the bank or investment pays you a reward for letting them use your money. This reward is called interest.

On the flip side, when you borrow money (like a loan), you pay interest to the lender.

There are two main types of interest you need to know:

Simple interest , calculated only on the original amount
Compound interest , calculated on the original amount plus any interest already earned

Analogy

Think of simple interest like earning a fixed salary every week , you always get the same amount. Compound interest is more like a snowball rolling downhill , it picks up more snow (money) as it grows, so it gets bigger and bigger over time.

Note

Why study this in Sciences? Interest is a perfect real-world example of two types of growth that appear throughout science:

Linear growth (like simple interest) , the same amount is added each time period. You see this in constant-speed motion or steady dripping of water.
Exponential growth (like compound interest) , the amount added each period keeps increasing. You see this in population growth, bacterial reproduction, and even radioactive decay (in reverse). Understanding these two patterns is a core scientific skill!

Simple Interest

Simple Interest: Simple interest is calculated as a fixed percentage of the original amount (called the principal) for each time period.

The formula for simple interest is:

$I = P \times r \times t$

Where:

$I$ = interest earned
$P$ = principal (the original amount invested or borrowed)
$r$ = annual interest rate (as a decimal, so 5% becomes 0.05)
$t$ = time (in years)

The total amount after $t$ years is:

$A = P + I = P (1 + r t)$

Note

With simple interest, the same amount of interest is added every year. If you earn $$$ 200 interest in year one, you will earn exactly $$$ 200 in year two, and so on. This produces linear growth , if you plotted it on a graph, you would get a straight line.

Example

Example: Sarah invests $$$ 3000 at a simple interest rate of 5% per year for 4 years. How much interest does she earn? What is the total amount?

Step 1: Identify the values.

$P = 3000$ , $r = 0.05$ , $t = 4$

Step 2: Calculate interest.
$I = 3000 \times 0.05 \times 4 = 600$

Step 3: Calculate total amount.
$A = 3000 + 600 = 3600$

Sarah earns $$$ 600 in interest and has $$$ 3600 in total after 4 years.

Free preview

10 more sections in this topic

Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.