Simple Interest Formulas

Complete mathematical formulas for simple interest calculations and financial computations

Basic Simple Interest Formula

Standard Formula

Where:

  • SI = Simple Interest
  • P = Principal amount (initial investment or loan)
  • R = Annual interest rate (as a percentage)
  • T = Time period (in years)

Decimal Rate Formula

Where r is the annual interest rate expressed as a decimal (e.g., 5% = 0.05).

Total Amount Formula

Where A is the total amount after adding simple interest to the principal.

Derived Formulas

Calculate Principal (P)

Calculate Rate (R)

Calculate Time (T)

Calculate Interest (SI)

Time Period Conversions

Common Time Conversions

Years to Other Units

  • 1 year = 12 months
  • 1 year = 52 weeks
  • 1 year = 365 days (non-leap)
  • 1 year = 366 days (leap year)

Fraction Conversions

  • 6 months = 0.5 years
  • 3 months = 0.25 years
  • 9 months = 0.75 years
  • 18 months = 1.5 years

Time in Days

For exact calculations, use 365 days for regular years and 366 for leap years.

Time in Months

Interest Rate Variations

Monthly Interest Rate

Where:

  • Rmonthly = Monthly interest rate
  • Tmonths = Time in months

Daily Interest Rate

Daily interest rate is typically calculated as: Rdaily = Rannual / 365

Converting Annual Rate to Other Periods

Multiple Investments

Different Principals, Same Rate and Time

Same Principal, Different Rates

Different Time Periods

Comparative Analysis Formulas

Ratio of Simple Interests

Equal Simple Interest Condition

For two investments to yield equal simple interest:

Doubling Time

Time required for principal to double under simple interest:

This formula gives the time in years when the interest equals the principal.

Tripling Time

Time required for principal to triple:

Formula Applications

Example 1: Basic Calculation

Given: P = $5000, R = 6% per annum, T = 3 years

Find: Simple Interest and Total Amount

Example 2: Finding Principal

Given: SI = $450, R = 5%, T = 2 years

Find: Principal

Example 3: Finding Rate

Given: P = $8000, A = $9200, T = 2.5 years

Find: Interest Rate