Simple Interest - Definition, Formula, Examples

Introduction to Simple Interest

• Simple interest is a method to calculate interest on a sum at a given rate for a set period.
• Unlike compound interest, the principal amount in simple interest remains the same throughout.
• Key terms: principal, rate of interest, time period.

What is Simple Interest?

• Interest applied to the original principal amount with a constant rate over each time cycle.
• Commonly used by banks for loans, including home, car, education, and personal loans.

Simple Interest Formula

• Formula: ( SI = \frac{P \times R \times T}{100} )
  • ( P ): Principal
  • ( R ): Rate of Interest (in % per annum)
  • ( T ): Time in years
• Alternative: ( SI = P \times R \times T ), where ( R ) is a decimal (e.g., 5% = 0.05).
• Amount Formula:
  • ( A = P + SI )
  • ( A = P + PRT )
  • ( A = P(1 + RT) )

Calculating Simple Interest

• Substitute ( P ), ( R ), and ( T ) into the formula to find simple interest.
• Example: Borrowing $1,000 at 5% for different years:
  • 1 Year: SI = $50, Amount = $1,050
  • 2 Years: SI = $100, Amount = $1,100
  • 3 Years: SI = $150, Amount = $1,150
  • 10 Years: SI = $500, Amount = $1,500

Types of Loans Using Simple Interest

• Simple interest is often used for short-term loans (1 month to 6 months).
• Interest can be calculated daily or weekly.
• Example: Borrow $10,000 at 10% per annum results in $2.73 per day.

Simple Interest vs Compound Interest

• Simple Interest:
  • Calculated on the original principal.
  • Formula: ( SI = P \times R \times T )
• Compound Interest:
  • Calculated on the principal plus accumulated interest.
  • Formula: ( CI = P(1 + R)^T - P )

Important Notes

• SI formula uses percentage unless ( R ) is expressed as a decimal.
• Interest from compound interest is always higher than simple interest.
• Compound interest methods are derived from simple interest.

Examples

1. Robert's Car Loan:
   • Principal: $48,000
   • Rate: 10%
   • Time: 4 Years
   • Amount to pay: $67,200
2. Maria's Loan:
   • Principal: $46,500
   • Rate: 20%
   • Time: 21 Months
   • Simple Interest: $16,275
3. Investment at 5% for 4 Years:
   • Amount: $3,500
   • Principal: $2,916.67

FAQs on Simple Interest

• Definition: Interest on initial amount without compounding.
• Use: Suitable for short-term financial calculations.
• Formulas:
  • Simple interest: ( PRT )
  • Compound interest: ( P(1 + R)^T - P )
• Types: Ordinary (365 days) and Exact (366 days in leap year).
• Home Loans: Usually use compound interest due to long terms.
• Car Loans: Typically use simple interest.

Practice Questions

1. Calculate extra return for a $1,000 loan at 5% after 2 years.
2. Determine the sum returned for $2,140 interest over 2.5 years at 16%.

Related Topics

• Future Value Simple Interest Formula
• Interest Rate Formula
• Total Interest Formula