Simple Interest: Definition, Formula, Examples

Introduction

• Simple interest is a method to calculate interest charged on a principal sum at a given rate over a period.
• Unlike compound interest, the principal remains unchanged in simple interest.
• Key terms: principal, amount, rate of interest, and time period.

What is Simple Interest?

• Interest applied only on original principal, with a consistent rate over time.
• Used by banks to pay interest on deposits or calculate loan interest.
• Loans: amounts borrowed from financial entities, repayable with interest.

Simple Interest Formula

• Formula: ( S.I. = \frac{P \times R \times T}{100} )
  • ( P ) = Principal
  • ( R ) = Rate of Interest (as percentage per annum, converted to a fraction for the formula)
  • ( T ) = Time in years
• Can also be expressed as ( S.I. = P \times R \times T ) when ( R ) is in decimal form.
• Total Amount = Principal + Simple Interest: ( A = P + PRT )

Calculating Simple Interest

• Substitute ( P, R, T ) in the formula to find ( S.I. ).
• Example: Borrowing $1,000 at 5% interest for different years.
  • 1 year: ( S.I. = 50 ), Amount = $1,050
  • 2 years: ( S.I. = 100 ), Amount = $1,100
  • 3 years: ( S.I. = 150 ), Amount = $1,150
  • 10 years: ( S.I. = 500 ), Amount = $1,500

Types of Loans Using Simple Interest

• Typically used for short-term loans (1-6 months).
• Interest calculated on a daily/weekly basis.
• Example: $10,000 loan at 10% per annum = $2.73 extra per day.

Simple vs Compound Interest

• Simple Interest
  • Calculated on original principal every time.
  • Formula: ( S.I. = P \times R \times T )
• Compound Interest
  • Calculated on accumulated principal and interest.
  • Formula: ( C.I. = P(1 + R)^T - P )

Important Notes

• Rate as percentage: ( \frac{PRT}{100} ).
• Rate as decimal: ( PRT ).
• Compound interest yields more interest than simple interest.

Examples

1. Car Purchase Example

   • Principal = $48,000, Rate = 10%, Time = 4 years
   • Amount = ( 48000(1 + 0.10 \times 4) = $67,200 )

2. Loan Example

   • Principal = $46,500, Rate = 20%, Time = 21 months
   • Simple Interest = $16,275

3. Investment Example

   • Aim to earn $3,500 at 5% for 4 years.
   • Principal = $2,916.67

Practice Questions

• Example problem: Calculate extra amount returned on a $1,000 loan at 5% for 2 years.

FAQs

• Definition: Interest calculated solely on initial amount.
• Use: Suitable for short-term loans, savings, monthly amortization.
• Types: Ordinary and exact simple interest.
• Interest Calculation: ( SI = P \times R \times T ).
• Monthly Calculation: Divide annual interest by 12.
• Rate Formula: ( R = \frac{SI \times 100}{P \times T} ).

Related Topics

• Future Value Simple Interest Formula
• Total Interest Formula
• Simple Interest Worksheets

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This document outlines the basics of simple interest, providing a comprehensive guide on definition, calculation, and application in various financial contexts.