11th Grade Q1

Understanding the difference between simple and compound interest is important in finance. Here’s how they differ:

1. Simple Interest

Interest is calculated only on the original principal (the starting amount).

The formula is:

where:

• $I$ is the interest,
• $P$ is the principal,
• $r$ is the annual interest rate (in decimal form),
• $t$ is the time (in years).

2. Compound Interest

Interest is calculated on the principal plus any previously earned interest.

The formula is:

where:

• $A$ is the total amount (principal + interest),
• $P$ is the principal,
• $r$ is the annual interest rate (in decimal form),
• $t$ is the time (in years).

Key Differences

• Simple interest grows linearly because it’s only based on the original principal.
• Compound interest grows exponentially because interest is added to the principal each year.

Example:

You invest $1,000 at an annual interest rate of $5\%$ for 3 years.

Using Simple Interest

The formula is:

Substitute the values:

So, the total amount is:

Using Compound Interest

The formula is:

Substitute the values:

Summary

• With simple interest, the total is $1,150$.
• With compound interest, the total is $1,157.63$.
• Compound interest gives more money because it grows faster over time.