DISCOUNT

                                                              DISCOUNT

Market price – The printed price or the tagged price of an article is called its marked price. It is also called the list price.

Discount – Discount is the amount allowed as rebate by a dealer to a customer on the marked price of the article. Discount is generally given as per cent.

Net Price – The selling price at which the article is sold to the customer after deducting the discount from the marked price is called the net price.

Formulae –

                                S.P. = M.P. – Discount

                               

                                Rate of discount = Discount% =

                                S.P. = M.P.

                                M.P. =

                               

SIMPLE INTEREST

                                                      SIMPLE INTEREST

Simple interest – The interest is the extra money which is paid by the borrower for the benefit of using the lender’s money.

Principal – The money borrowed from a lender is called principal.

Interest – The additional money paid by the borrower to the lender after a specified period of time is called interest.

                Or, The extra money paid for using the principal is called the interest.

Amount – The total money paid by the borrower to the lender is called amount.

                Or, The total money which is received or paid back is called amount.

                               

                                Amount = Principal + Interest

Time – the period after which the amount is to paid back is called the time.

                                Suppose, we deposit ₹1,000 for three years at the rate of ₹150of interest per year in a bank. It means the bank will have to pay us extra ₹150 at the end of first year, ₹150 at the end of second year and ₹150 at the end of third year.

                Thus, after three years:

                                                Principal = ₹1,000

                                                Interest = ₹150 + ₹150 + ₹150 = ₹450

                                                Amount = Principal + Interest

                                                                  = ₹1,000 + ₹450 = ₹1,450. 

Rate of Interest – The rate of interest is usually expressed in percentage.

                                An interest rate of ‘8% per year’ means the borrower has to pay ₹8 as interest for the loan of ₹100 at the end of one year.

ð  We also write ‘annual’ for ‘per year’.

ð  As the rate of interest is usually expressed in ‘per year’, we generally do not write ‘per year’ against the rate of interest.

Calculating interest –

                The interest depends on the principal, the rate of interest and time period for which the money is borrowed or deposited.

                Suppose, we have to calculate simple interest on ₹500 for 3 years at 10% per year.

                                Now, interest on ₹100 for 1 year = ₹10 (rate 10%)

                                           interest on ₹1 for 1 year = ₹

                                 interest on ₹500 for 1 year = ₹

                                 interest on ₹500 for 3 years = ₹

                        Here, we see that the interest is calculated as

                                                                Simple interest = ₹

                                                                        I = ₹

Ø  In this formula, R is in ‘per cent per year’ and T is in years.

Formulae - 

                               

                               

                               

                               

                               

                                   

PROFIT AND LOSS

                                                       PROFIT AND LOSS

Cost price (C.P.) - The price at which a dealer buys an article is called the cost price.

Selling price (S.P.) – The price at which a dealer sells an article is called the selling price.

When S.P. > C.P.,  then profit = S.P.;

        Profit% =

When S.P. < C.P.,  then loss = C.P. – S.P.;

       

        Loss% =

S.P. =                  or              S.P. =

C.P. =                   or              C.P. =

PERCENTAGE

                                                                         PERCENTAGE

                                               

                Per cent means per hundred or for every hundred. The symbol % is used to denote per cent, i.e., 48 marks out of 100 is 48%.

                A fraction with denominator 100 such as  is called a percent. The numerator tells the percentage.

To convert –

      (i) A fraction into a per cent, multiply the fraction by 100, e.g.,

     (ii) A ratio into a per cent, write it as a fraction and multiply the fraction by 100,

                 e.g.-

     (iii) A decimal into a per cent, multiply by 100, i.e., shift the decimal point two places to the right,

                 e.g.- 0.025 =(0.025 )% = 2.5%

     (iv) A per cent into a fraction, drop the per cent symbol (%) and divide by 100,

                 e.g.- 40% = .

(v) A per cent into a ratio, drop the per cent symbol and form a ratio with the number obtained after dropping             the symbol as the first term and 100 as the second term, e.g., 65% =

     (vi) A per cent into a decimal, drop per cent symbol and shift the decimal point two places to left,

                          e.g.- 95% = 0.95, 4.35% = 0.0435.

To find what per cent the first number is of second,

                Divide the first number by the second number and multiply the result by 100. First ensure that the numbers are in the same units, i.e., 3 hours as a percentage of

2 days   

                                Increase % =

                                Decrease % =

                                Error % =