### 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. =

''                           ''

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

S.I. =

IMPORTANT FORMULAE FOR SIMPLE INTEREST

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

S.I. = Pn

RT = n × 100

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

P + S.I. = Pn

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% —

IMPORTANT FORMULAE FOR COMPOUND INTEREST

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

⇒ If rate is fixed, then

(n → Number of years)

⇒ If time is in different form, then

{Where F → Fraction part of time}

F = or

⇒ C.I. = A – P

=

⇒ If two amount is given, then

⇒ If amount of two continuous year is given then,

r =

⇒ 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

(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.

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

⇒ Difference between compound interest and simple interest :-

⇒ C.I. =

S.I. =

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

=

(i) If t = 2 years then

diff. =

(ii) If t = 3 years then

diff =

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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