What is Simple and Compound Interest

Simple Interest

Definition: Simple interest is the interest calculated on the original principal amount for a specific period at a fixed rate of interest.

Formula: Simple Interest (SI) = (P × R × T)/100​

Where:

• P = Principal amount (the initial amount of money)
• R = Rate of interest per annum (in percentage)
• T = Time the money is borrowed or invested for (in years)

Example: Suppose we invest $1,000 at an interest rate of 5% per annum for 3 years.

Using the formula: SI=(1000×5×3)/100=150

So, the simple interest earned over 3 years is $150.

The total amount after 3 years would be:

Total Amount= Principal+Simple Interest=1000+150=1150

Compound Interest

Definition: Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.

Formula: Compound Interest (CI)=P(1+R/100)^T−P

Where:

• P = Principal amount
• R = Rate of interest per annum (in percentage)
• T = Time the money is invested or borrowed for (in years)

Example: Suppose we invest $1,000 at an interest rate of 5% per annum, compounded annually, for 3 years.

Using the formula: Total Amount=1000(1+5/100)^T=1000(1.05)³

Total Amount=1000×1.157625=1157.625

So, the compound interest earned over 3 years is:

CI=1157.625−1000=157.625

Comparison

• Simple Interest: The interest is calculated on the original principal amount only.
• Compound Interest: The interest is calculated on the principal amount plus any interest previously earned.

Visual Representation:

• Simple Interest: If we imagine stacking blocks where each block represents $50, with simple interest, we add the same size block every year.
• Compound Interest: Each block starts small, but every year, the next block gets bigger because it’s added on top of the previous blocks.

Summary

• Simple Interest: Best for short-term investments where interest isn’t expected to grow over time.
• Compound Interest: Better for long-term investments where interest grows exponentially over time, leading to potentially higher returns.