Compound interest and simple interest are two different methods of calculating interest on a principal amount.

Compound interest and Simple interest differences

1. Calculation Basis

• Simple Interest (SI):
  • Interest is calculated only on the principal amount (initial amount).
  • Formula: SI=P×R×TSI = P \times R \times TSI=P×R×T
  • Where:
    • PPP = Principal amount
    • RRR = Annual interest rate
    • TTT = Time period (in years)
• Compound Interest (CI):
  • Interest is calculated on the principal amount and also on the accumulated interest of previous periods.
  • Formula: CI=P(1+Rn)nT−PCI = P \left(1 + \frac{R}{n}\right)^{nT} – PCI=P(1+nR​)nT−P
  • Where:
    • PPP = Principal amount
    • RRR = Annual interest rate
    • TTT = Time period (in years)
    • nnn = Number of times interest is compounded per year

2. Interest Growth

• Simple Interest:
  • Grows linearly over time.
  • The amount of interest remains constant for each period.
• Compound Interest:
  • Grows exponentially over time.
  • The amount of interest increases in each period because interest is earned on previously accumulated interest.

3. Total Interest Earned

• Simple Interest:
  • Typically results in less interest earned compared to compound interest over the same period.
• Compound Interest:
  • Results in more interest earned due to the effect of compounding, especially over long periods.

4. Use Cases

• Simple Interest:
  • Commonly used in loans, short-term investments, and some savings accounts where interest calculations are straightforward and timeframes are shorter.
• Compound Interest:
  • Commonly used in savings accounts, investments, and loans where interest can compound frequently, such as annually, semi-annually, quarterly, monthly, or daily.

Examples

1. Simple Interest Example:
   • Principal (PPP) = $1,000
   • Annual Interest Rate (RRR) = 5%
   • Time (TTT) = 3 years
   • SI = 1000 \times 0.05 \times 3 = $150
   • Total amount after 3 years = Principal + Interest = $1,000 + $150 = $1,150
2. Compound Interest Example (compounded annually):
   • Principal (PPP) = $1,000
   • Annual Interest Rate (RRR) = 5%
   • Time (TTT) = 3 years
   • Compounded annually (nnn) = 1
   • CI = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3} – 1000 = 1000 \left(1.05\right)^3 – 1000 = 1000 \times 1.157625 – 1000 = $157.63
   • Total amount after 3 years = Principal + Interest = $1,000 + $157.63 = $1,157.63

Understanding these differences helps in making better financial decisions, whether you’re saving, investing, or borrowing money.

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