Compound interest is a concept in finance where interest is calculated on the initial principal amount as well as on the accumulated interest from previous periods. Here’s how compound interest works:

1. Initial Principal Amount:

   • You start with an initial amount of money, known as the principal.

2. Interest Rate:

   • There is an agreed-upon interest rate, which is a percentage of the principal that will be added to the amount at regular intervals.

3. Compounding Period:

   • Compound interest can be calculated at different intervals, such as annually, semi-annually, quarterly, monthly, or daily. The more frequent the compounding, the more interest you will earn.

4. Calculation:

   • At the end of each compounding period, the interest is calculated based on the total amount (principal + interest earned so far).
   • The interest earned during that period is added to the principal for the next period’s interest calculation.

5. Accumulation:

   • Over time, the interest earned in each period accumulates, leading to exponential growth in the total amount.

6. Formula:

   • The formula for calculating compound interest is: A = P(1 + r/n)^(nt)
     • A: Total amount after t years
     • P: Principal amount
     • r: Annual interest rate (in decimal form)
     • n: Number of compounding periods per year
     • t: Number of years

7. Example:

   • Let’s say you invest $1,000 at an annual interest rate of 5% compounded annually for 3 years.
   • Using the compound interest formula: A = 1000(1 + 0.05/1)^(1*3) = $1,157.63
   • After 3 years, your investment would grow to $1,157.63 with compound interest.

Compound interest allows your money to grow faster over time compared to simple interest because you earn interest on both the initial principal and the accumulated interest. It’s a powerful concept in finance that can help individuals and businesses grow their wealth over the long term.