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