Simple and Compound Interest Concepts

Simple Interest (SI)

• Simple interest is calculated only on the principal amount.

• It does not accumulate on the interest earned in previous periods.

• The formula for calculating simple interest is: SI = (P * R * T) / 100, where:

  • P = Principal amount
  • R = Rate of interest per year
  • T = Time period in years

• Example: If a principal amount of $1000 is invested at a rate of 5% per year for 2 years, the simple interest is calculated as: SI = (1000 * 5 * 2) / 100 = $100. The total amount after 2 years would be $1100 (principal + interest).

Compound Interest (CI)

• Compound interest is calculated on both the principal and the accumulated interest from previous periods.

• It's a form of interest that "compounds" or builds on itself over time.

• Interest is calculated periodically (daily/monthly/annually etc), and added to the principal

• The effective interest rate may differ depending on the compounding frequency. For a given nominal interest rate, higher compounding frequency leads to a higher effective interest rate.

• The formula for calculating compound interest can be complex, but a common formula using the exponent function (e) for continuous compounding may also be used.

• Example: If a principal amount of $1000 is invested at a rate of 5% per year for 2 years compounded annually, the compound interest would be calculated as follows:

  • Year 1: Interest = (1000 * 5) / 100 = $50. New principal = $1000 + $50 = $1050
  • Year 2: Interest = (1050 * 5) / 100 = $52.50. New principal = $1050 + $52.50 = $1102.50, a higher result compared to simple interest.

• Formulas for Compound Interest

  • For n periods of compounding: A = P(1 + r/n)^(nt)
    • A = Final amount
    • P = Principal amount
    • r = annual interest rate (as a decimal)
    • n = number of times interest is compounded per year
    • t = number of years.
  • For continuous compounding: A = Pe^(rt)
    • A = Final amount
    • P = Principal amount
    • r = annual interest rate (as a decimal)
    • t = number of years
    • e ≈ 2.718 is Euler's constant.

Key Differences between SI and CI

• Basic Principle: Simple interest (SI) is calculated only on the principal, while compound interest (CI) is calculated on both the principal and the accumulated interest.
• Profitability: Compound interest generally yields a higher return over a longer time period due to the compounding effect.
• Compounded Interest Calculation: Compound interest involves successive computations of interest, making it more complex than simple interest computation.
• Usage in Real World: Simple interest is relatively easier to calculate and so may be simpler for certain financial transactions. Compound interest is more common in long-term investments and savings accounts due to its compounding effect on returns.
• The choice between simple and compound interest methods depends on the specific financial goals and circumstances.