Simple Interest.......[competitive. exam prep.... topic 36].

'Simple Interest' A quick method of calculating the interest charge on a loan. Simple interest is determined by multiplying the interest rate by the principal by the number of periods. Where: P is the loan amount I is the interest rate N is the duration of the loan, using number of periods.


Formulae & Examples

Formula for finding out Simple Interest


  1. Principal: The money borrowed or lent out for a certain period is called the principal or thesum.
  2. Interest: Extra money paid for using other's money is called interest
  3. Simple Interest (S.I.):.If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.
Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then


  • . Simple Intereest = ((P*R*T)/100)
  • .P = ((100*S.I)/R*T); R = ((100*S.I)/(P*T)) and T = ((100*S.I)/(P*R)
     4.Calculate Total Amount Accrued (Principal + Interest)



  • A = P(1 + rt)

      5. Calculate Principal Amount, solve for P
  •    P = A / (1 + rt)

       6. Calculate rate of interest in decimal, solve for r
   r = (1/t)(A/P - 1)

       7. Calculate rate of interest in percent
   R = r * 100

      8. Calculate Total Amount Accrued (Principal + Interest)
   A = P(1 + rt)
               
       
Sample Example
Ex

  • Mohan borrowed some money at the rate of 5 % p. a. for the first two years, at a rate of 8 % p. a for the next three years, and at the rate of 10 % for the period beyond five years.. If he pays total interest of Rs. 12500 at the end of 8 years, how much mony did he borrows ?

Let P be the sum borrowed

    ((P*5*2)/100)+((P*8*3)/100)+((P*10*3)/100)= 12500, P = 199531.25

Ex
  • A sum of money doubles itself in 8 years at simple interest. What is the rate of interest ?
Let the Sum is Rs 100, after 8 years it will become 200
    So Interest will be = 200 - 100 = 100 , so the rate of interest will be :

    RI = ((100*SI)/(P*T)) = ((100*100)/(100*8)) = 12.5% 

Ex

  • A sum of money amounts to Rs. 9800 after 5 yers and Rs. 12005 after 8 years at the same rate of simple interest. What is the rate of interest per annum ?

Simple interest for 8 years - Simple interest of 5 years = Simple interest for 3 years = 12005 - 9800 = 2205
    Principle = (9800 - 3675) = 6125, RI = ((100*3675)/(6125*5)) = 12 %

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