Formulas For Simple Interest And Compound Interest Problems

Definition of Compound Interest

Compound interest is the addition of interest to the principal sum of a loan or deposit. Compound interest is calculated based on the principal, interest rate, and the time period involved.

Definition of Simple Interest

The interest calculated on the amount initially invested or loaned. It is a method for calculating the interest earned or paid on a certain balance in a specific period.

Simple Interest_Compound Interest_formula

Formula for Compound Interest

Interest Compounded Annually

  • Amount = P (1+r/100)t
  • Compound Interest = Total amount – Principal
  • Rate of interest (R) = [(A/P)1/ t − 1] %

Interest Compounded Half-Yearly

  • Amount = P (1+r/2/100)2t
  • Compound Interest = Total amount – Principal
  • Rate of interest (R) = 2*[P1/t − 1] %

Interest Compounded Quarterly

  • Amount = P (1+r/4/100)4t
  • Compound Interest = Total amount – Principal

Interest is Compound Monthly

  • Amount = P (1+r/12/100)12t

Interest is Compounded Annually but Time is in Fraction, say 2(3/2) years

  • Amount = P (1+r/100)2 * (1+(3/2)r/100)

CI when Rates are Different for Different Years

  • Amount = P (1+r1/100) (1+r2/100) (1+r3/100)

Formula for Simple Interest

Simple Interest

SI = P*r*t/100


P = money borrowed or lent out for a certain period

r = rate of interest
t = time period for which the amount is lent

  • Principal = 100* SI/ R * T
  • Rate = 100* SI/ P * T
  • Time = 100* SI/ R * P

Total Amount of Money

Amount = Principal + Interest

A = P + I

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