PROFIT LOSS & INTEREST

ALL IMPORTANT FORMULAE RELATED  TO 

1>. BASIC INTRODUCTION
2>. PROFIT & LOSS
3>. SIMPLE INTEREST
4>. COMPOUND INTEREST

1.  BASIC INTRODUCTION_

• Cost Price (क्रय मूल्य ): -The price, at which an object is purchased, is called its cost price, It is denoted by C.P.
• Selling Price (विक्रय मूल्य ):- The price, at which an object  is sold, is called its selling price, It is denoted by S.P.
• Profit or Gain (लाभ):- If S.P. is greater than C.P. ( SP>CP), the seller is said to have a profit or gain.
• Loss(हानि):- If S.P. is less than C.P.(SP<CP), the seller is said to have incurred a loss.
• Discount(बट्टा या छूट) :-A deduction from the usual cost of something is called discount.
• Principal(मूलधन):- The money borrowed or lent out for a certain period is called the principal or the sum.
• Interest(ब्याज):- Extra money paid for using other's money or  on principal money is called interest.
• Rate of interest (ब्याज की दर) :- The rate at which the money borrowed or lent out for a certain period is called rate of interest.
• Amount(मिश्रधन):- The sum of principal money and interest is called amount.
• Compound interest (चक्रवृद्धि ब्याज):- It is special type of of simple interest .Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words,interest on interest.

  2. PROFIT & LOSS_

1. Gain = (S.P.) - (C.P.)
2. Loss = (C.P.) - (S.P.)
3. Loss or gain is always reckoned on C.P.
4. Gain Percentage: (Gain %)

   Gain % =		Gain x 100
   		C.P.

5. Loss Percentage: (Loss %)

   Loss % =		Loss x 100
   		C.P.

6. Selling Price: (S.P.)

   SP =		(100 + Gain %)	x C.P
   		100

7. Selling Price: (S.P.)

   SP =		(100 - Loss %)	x C.P.
   		100

8. Cost Price: (C.P.)

   C.P. =		100	x S.P.
   		(100 + Gain %)

9. Cost Price: (C.P.)

   C.P. =		100	x S.P.
   		(100 - Loss %)

10. If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.

Ex- If an book is sold at a gain of 20 % and if the actual price of book is 200 ruppes ,then Its selling price will be S.P. = 120 % of C.P. = 240 

OTHER FORMULE

1. If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.
2. If an article is sold at a loss of say, 35% then S.P. = 65% of C.P.
3. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:

   Loss % =		Loss and Gain %		2	=		x		2	.
   		10					10
4. If a trader professes to sell his goods at cost price, but uses false weights, then

   Gain % =		Error	x 100	%.
   		(True Value) - (Error)

5. If cost price of one thing (no of item = X) is equal to selling price of another thing(no of item =y ) 

then, CP=y and SP=xCP/SP =y/x.( Divide it and take it in simplest form, don't divide completely)
Now if y > X , then we have profit = y-x
Or if x > y ,then we have loss = x-y
Then Total profit/loss % can be calculated simply by using basic formula.

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3. SIMPLE INTEREST 

1. Principal:
   The money borrowed or lent out for a certain period is called the principal or the sum.
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

   (i). Simple Intereest =		P x R x T
   		100

   (ii). P =

   100 x S.I.

   ; R =

   100 x S.I.

   and T =

   100 x S.I.

   .

   R x T

   P x T

   P x R

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4. Compound interest 

1. Let Principal = P, Rate = R% per annum, Time = nyears.
2. When interest is compound Annually:

   Amount = P		1 +	R		n
   			100

3. When interest is compounded Half-yearly:

   Amount = P		1 +	(R/2)		2n
   			100

4. When interest is compounded Quarterly:

   Amount = P		1 +	(R/4)		4n
   			100

5. When interest is compounded Annually but time is in fraction, say 3 years.

   Amount = P		1 +	R		3	x		1 +	R
   			100						100

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

   Then, Amount = P

   1 +

   R1

   1 +

   R2

   1 +

   R3

   .

   100

   100

   100

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

   Present Worth =	x	.
   	1 + R 100

   Thanks
   Rahul Kumar
   
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