Cheatsheet: Interest | General Aptitude for GATE - Mechanical Engineering PDF Download

Theory

Simple Interest is the interest earned when the borrower usually pays a fee to the lender each year and that fee is usually a percentage of amount borrowed at the start.
Compound Interest is the interest earned on the initial principal plus the interests earned over the previous periods of the loan.

Formula

• If a sum of money becomes x-times of itself in T-years @ R% p.a. S.I. then  (x -1)100 = T×R
• If a sum of money becomes x₁-times of itself in a time of T₁-years @ R₁% p.a.
  S.I. it becomes x₂-times of itself in T₂-years @ R₂% p.a. S.I. then
• A sum (P) of money becomes an amount of A₁ in T₁ years at a certain rate and the same sum becomes an amount of  A₂ in T₂ years (T₂ > T₁). Then P =  and the rate  
• If the rates of compound interest are R₁ , R₂ , R₃ ……….. R_n for n-successive years then
  
• If a sum of Rs P is lent out at R% p.a. compound interest for n-years then
   , if the interest is compounded half-yearly
  , if the interest is compounded quarterly
• The difference between compound interest and simple interest on a sum of Rs P for 2-years at R% p.a. is given by
  Also , where S.I is simple interest for 2 years
• The difference between compound interest and simple interest on a sum of Rs P for 3  years at R% p.a. is given by  where S.I. is simple interest for 3-years
• If a sum of money amounts to A_n−1 and to A_n in (n – 1) and n years respectively then
    

Solved Example