COMPOUND INTREST

                                                   COMPOUND INTEREST

* While calculating compound interest, the simple interest which is calculated for the principal of first year will add to the principal which we taken already.

* The addition of this amount will be the principal for second year. It will go on increase like this. Finally principal is subtracted from last year amount. The result of this subtraction gives compound interest. It is denoted by 'CI'.

Basic Formulas:

Let Principal = P

Rate = R% per annum

Time = n years

* When interest is compound Annually:  Amount = P*[1+ ( R /100)]˄n

* When interest is compounded Half-yearly: Amount= p*[1+ (R/2) / 100]˄2n

* When interest is compounded Quarterly: Amount = P*[1+((R/4) /100)]˄4n

* When interest is compounded Annually but time is in fraction , say 4(2/5)years:

   Amount = {P * [1+ (R/100) ] 4} * [1+ (( 2R/5 ) / 100) ]

*When Rates are different for different years, say R1% , R2%, R3% for 1^st, 2^nd, 3^rd year respectively. 

  Amount = P*[1+(R1/100)] * [1+ (R2/100)] * [1+ (R3/100)]

*Present worth of Rs.x due n years hence is given by:

  Present worth = x / [1+ (R/100) ]˄n

Example  sum

1) A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

A. Rs. 120 B. Rs. 121 C. Rs. 122 D. Rs. 123 Explanation: Amount = Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5 2 x 100 2 x 100 = Rs. 1600 x 41 x 41 + 1600 x 41 40 40 40 = Rs. 1600 x 41 41 + 1 40 40 = Rs. 1600 x 41 x 81 40 x 40 = Rs. 3321.  C.I. = Rs. (3321 - 3200) = Rs. 121

2) The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: A. 625 B. 630 C. 640 D. 650   Explanation: Let the sum be Rs. x. Then, C.I. = x 1 + 4 2 - x = 676 x - x = 51 x. 100 625 625   S.I. = x x 4 x 2 = 2x . 100 25   51x - 2x = 1 625 25  x = 625.   3)There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate? explanation: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.  R = 100 x 60 = 10% p.a. 100 x 6 Now, P = Rs. 12000. T = 3 years and R = 10% p.a.  C.I. = Rs. 12000 x 1 + 10 3 - 1 100 = Rs. 12000 x 331 1000 = 3972.