Simple and Compound Interest

Simple Interest

• Simple interest is calculated only on the principal amount.
• The interest earned in each period is the same.
• Formula: Simple Interest (SI) = (Principal × Rate × Time) / 100
• Principal is the initial amount of money.
• Rate is the interest rate per year (as a percentage).
• Time is the duration of the investment in years.
• Example: If $1000 is invested at 5% simple interest for 2 years, the simple interest earned is $100.

Compound Interest

• Compound interest is calculated on the principal and the accumulated interest from previous periods.
• The interest earned grows exponentially over time.
• Interest is compounded at regular intervals (e.g., annually, semi-annually, quarterly, monthly).
• Formula for compound interest: Future Value (FV) = P (1 + r/n)^(nt)
  • P = Principal amount
  • r = annual interest rate (as a decimal)
  • n = number of times interest is compounded per year
  • t = number of years the money is invested or borrowed for
  • FV = future value of the investment/loan, including interest.
• Example: If $1000 is invested at 5% compound interest compounded annually for 2 years, the future value is $1102.50.

Key Differences between Simple and Compound Interest

• Simple interest calculates interest only on the principal.
• Compound interest calculates interest on both the principal and accumulated interest.
• Compound interest generally yields a higher return over time due to earning interest on the interest.
• Simple interest does not earn interest on accumulated interest, making it less advantageous for long-term investments.

Applications of Simple and Compound Interest

• Savings accounts use compound interest to track savings growth.
• Loans use compound interest to calculate total interest paid.
• Investments use compound interest to determine growth over time.
• Business decisions rely on both simple and compound interest calculations.

Important Concepts

• Principal: The initial investment or loan amount.
• Interest Rate: The percentage of principal earned/charged yearly.
• Time: The duration of the investment or loan.
• Compounding Frequency: How often interest is calculated and added.
• Future Value: The total value after a period including interest.

Simple vs Compound Interest Calculation Examples

• These examples demonstrate compound interest's faster growth compared to simple interest over time. | Time Period (Years) | Simple Interest | Compound Interest | |---|---|---| | 1 | $50 | $50 | | 2 | $100 | $102.50 | | 3 | $150 | $107.56 | | 5 | $250 | $127.62 |