Compound Interest?

Compound interest is an interest paid on the initial principal and previously earned interest. In other words, it’s interest on interest.

Here’s a breakdown of how compound interest works:

1. Initial Principal (P): This is the original amount of money that you deposit or borrow.
2. Interest Rate (r): This is the percentage of the principal that is charged or paid over a certain period. It’s typically expressed as an annual percentage rate (APR).
3. Time (t): This is the amount of time the money is invested or borrowed, usually expressed in years.

The formula for compound interest is given by:

where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of times that interest is compounded per unit $t$ (usually per year).
• $t$ is the time the money is invested or borrowed for, in years.

The key difference between simple interest and compound interest is that in compound interest, the interest is added to the principal after each compounding period, and subsequent interest calculations are based on the updated principal.

For example, if you have $1,000 invested at an annual interest rate of 5%, compounded annually, after one year you would have $1,000 \times (1 + 0.05)^1 = $1,050. In the second year, the interest is calculated on $1,050 rather than the original $1,000. This compounding effect continues, leading to the exponential growth of the investment or debt over time.