Finance Math: Simple Interest

Introduction to Simple Interest

• Simple interest is less common today due to the higher returns possible with compounded interest.
• It's essential to understand the concept of simple interest.

Key Concepts

• Principal (P):
  • Initial amount of money invested.
  • For example, $1000 put in the bank.
• Interest:
  • The return on the principal investment.
  • Expressed in dollars.
• Accumulated Amount (A):
  • Total amount consisting of initial principal plus interest earned.
• Rate (R):
  • Interest rate, expressed as a percentage or decimal.
  • Higher rates mean more interest.
• Time (T):
  • Duration of the investment, usually in years.

Differences Between Simple and Compounded Interest

• Simple interest does not pay interest on previously earned interest.
• Compounded interest pays interest on the accumulated principal and interest.

Mathematical Definition

• Interest Earned (I):
  • Formula: ( I = P \times R \times T )
  • Result is in dollars.
• Accumulated Amount (A):
  • Formula: ( A = P + I = P \times (1 + R \times T) )

Example Calculation

• Given:
  • Principal (P): $2000
  • Interest Rate (R): 5% (0.05)
  • Time (T): 3 years
• Interest Calculation:
  • ( I = 2000 \times 0.05 \times 3 = 300 )
  • Earned $300 in interest over three years.
• Accumulated Amount Calculation:
  • ( A = 2000 + 300 = 2300 )
  • After three years, the accumulated amount is $2300.

Conclusion

• Simple interest is straightforward to calculate.
• Provides a clear example of interest calculation and accumulated amount.
• Important foundational concept before moving to more complex interest calculations like compounded interest.