Interest is the cost of borrowing money or the reward for saving it. Think of it like rent. If you borrow someone's apartment, you pay them rent. If you borrow someone's money, you pay them interest. On the flip side, if a bank uses your saved money, it pays you interest.

There are two main ways to calculate interest: simple and compound. They start similarly but end up in very different places.

Simple interest is calculated only on the original amount of money, known as the principal. It's a straightforward, fixed calculation. The amount of interest you earn or pay is the same every single period.

The formula for simple interest is:

$I = P \times r \times t$

Where:

• I is the Interest
• P is the Principal (the starting amount)
• r is the annual interest rate (as a decimal)
• t is the time in years

Let's say you borrow $1,000 at a 5% simple interest rate for 3 years. The interest calculation for each year is the same: $1,000 × 0.05 = $50.

After 3 years, you would owe $150 in interest, plus the original $1,000 principal, for a total of $1,150.

Compound interest is where things get interesting. It's calculated on the principal amount plus all the accumulated interest from previous periods. You earn interest on your interest.

Let's revisit our $1,000 investment, but this time with a 5% interest rate that compounds annually.

• Year 1: You earn $1,000 × 0.05 = $50. Your new balance is $1,050.
• Year 2: You earn interest on the new, larger balance: $1,050 × 0.05 = $52.50. Your new balance is $1,102.50.
• Year 3: You earn interest on that even larger balance: $1,102.50 × 0.05 = $55.13. Your final balance is $1,157.63.

With compound interest, you earned $7.63 more than with simple interest in just three years. The difference might seem small at first, but it grows dramatically over time.

The formula for the total amount ($A$) with compound interest is:

This formula calculates the final amount directly. To find just the compound interest, you subtract the principal from the final amount ($A - P$).

This graph shows why compounding is often called a miracle of finance. Over long periods, the accelerating growth of compound interest leaves simple interest far behind.

Now, let's test your understanding of these core concepts.

Understanding the difference between simple and compound interest is fundamental to making smart financial decisions, whether you're saving for the future or taking out a loan.