SI and CI

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   SIMPLE INTEREST:

⇒ Principal amount : the amount that is originally borrowed from someone or lent to someone, is called principal.

⇒ Interest (I) → the additional amount paid , for using the principal amount money , is called the interest.

⇒ Simple Interest (S.I.) → if interest is calculated equally for whole time , then interest is called Simple interest. 

⇒ (Amount) (A) → the combined amount of Principal and Interest is called Amount. it is the final value of money that is to be paid.

⇒ A = P + S. I. ⇒ S. I. = fraction numerator straight P cross times straight R cross times straight T over denominator 100 end fraction

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⇒ if the rate of interest is different for each year then :

     S.I. = fraction numerator straight P space left parenthesis straight r subscript 1 straight t subscript 1 plus straight r subscript 2 straight t subscript 2 plus straight r subscript 3 straight t subscript 3 plus... right parenthesis over denominator 100 end fraction

IMPORTANT FORMULAE FOR SIMPLE INTEREST

A) if interest becomes "n" times of principal amount then —

     S.I. = Pn

         PRT over 100 equals Pn

           RT = n × 100

B) If amount becomes "n" time of principal amount then  —

      P + S.I. = Pn

     PRT over 100 equals straight P left parenthesis straight n minus 1 right parenthesis

      RT = (n – 1) 100

 

⇒ when there is a change in Simple interest  due change in rate of interest then —

     

 P = 

 

⇒ Annual installment of Simple Interest →  the amount of installment that can repay the debt of P Rs.  at an annual rate of r% —

fraction numerator 100 space straight P over denominator open parentheses 100 space straight t plus begin display style fraction numerator straight r space straight t space left parenthesis straight t minus 1 right parenthesis over denominator 2 end fraction end style close parentheses end fraction

 

                                                                                                 IMPORTANT FORMULAE FOR COMPOUND INTEREST

 

⇒ If rate is different for C.I. of each years then

straight A space equals space straight P open parentheses fraction numerator 100 space plus space straight r subscript 1 over denominator 100 end fraction close parentheses open parentheses fraction numerator 100 space plus space straight r subscript 2 over denominator 100 end fraction close parentheses open parentheses fraction numerator 100 space plus space straight r subscript 3 over denominator 100 end fraction close parentheses......

⇒ If rate is fixed, then

straight A space equals space straight P open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight n (n → Number of years)

⇒ If time is in different form, then

straight A space equals thin space straight P open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight n open parentheses fraction numerator 100 space plus space rF over denominator 100 end fraction close parentheses {Where F → Fraction part of time}

F = Months over 12 or Days over 365

⇒ C.I. = A – P

= straight P open curly brackets open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight n space minus space 1 close curly brackets

⇒ If two amount is given, then

straight A subscript 2 over straight A subscript 1 space equals space open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight t subscript 2 minus straight t subscript 1 end exponent

⇒ If amount of two continuous year is given then,

r = open parentheses fraction numerator straight A subscript 2 space minus space straight A subscript 1 over denominator straight A subscript 1 end fraction close parentheses space cross times space 100

⇒ Installment at compound Interest

Theorem (1) :- A sum of Rs 'P' is to be paid back in n equal installments. If the interest is compound annually at R% per annum, then the value of each installment is given by

open square brackets fraction numerator straight P over denominator open parentheses begin display style fraction numerator 100 over denominator 100 space plus space straight R end fraction end style close parentheses space plus space open parentheses begin display style fraction numerator 100 over denominator 100 space plus space straight R end fraction end style close parentheses squared space plus space....... space plus space open parentheses begin display style fraction numerator 100 over denominator 100 space plus space straight R end fraction end style close parentheses to the power of straight n end fraction close square brackets

(2) A person buys an item on the terms that he is required to Rs P cash down payment followed by Rs. x at the end of first year, Rs y at the end of second year and Rs Z at the end of third year. Interest is charged at the rate of R% per annum, then the

(i) Cash price of the item is given by Rs. straight P space plus space open parentheses fraction numerator 100 over denominator 100 space plus space straight R end fraction close parentheses open square brackets straight x space plus space straight y open parentheses fraction numerator 100 over denominator 100 space plus space straight R end fraction close parentheses space plus space straight z open parentheses fraction numerator 100 over denominator 100 space plus space straight R end fraction close parentheses squared close square brackets

(ii) The total interest charged is given by Rs. [p + x + y + z – cash price]

⇒ Difference between compound interest and simple interest :-

⇒ C.I. = straight P open curly brackets open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight t space minus space 1 close curly brackets

S.I. = prt over 100

⇒ For 't' years diff. between C.I. and S.I.

= straight p open curly brackets open parentheses fraction numerator 100 space plus space straight r over denominator 100 end fraction close parentheses to the power of straight t space minus space 1 space minus space rt over 100 close curly brackets

(i) If t = 2 years then

diff. = straight p open parentheses straight r over 100 close parentheses squared

(ii) If t = 3 years then

diff = straight p open parentheses straight r over 100 close parentheses squared open parentheses fraction numerator 300 space plus space straight r over denominator 100 end fraction close parentheses

theorem 3) : if a some of money becomes  "x" times in "y" years then it will become "xn" times in "ny" years.

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