PERCENTAGES GATE 2020 STUDY MATERIAL PDF CIVILENGGFORALL

Percentage
Simple Interest and Compound Interest
Profit and Loss
Partnership
Stocks
Shares

The term percentage is quite frequently used in our day to day life especially to avoid the fractions less than 1. Instead of treating the complete entity as 1, we treat as 100, and take the ratios accordingly. The term Percentage means for every hundred. A fraction whose denominator is 100 is called percentage and numerator of the fraction is called rate per cent. It is denoted by the symbol %.

SIMPLE INTEREST AND COMPOUND INTEREST

When a sum of money is lent by A to B, A is called lender (creditor), B the borrower (debtor).
The sum lent is called principal (P).
Interest (I) is the extra money paid by the borrowed to the lender for the use of the money for a specified time.
The time for which the money is borrowed is called period (N).
The extra amount paid per 100 rupees in a year is called rate per cent per annum (R).
The sum of interest and principal is called Amount (A).

Simple Interest (S.I.)

When interest is paid as it falls due, it is called simple interest i.e., throughout the load period, interest is charged on the original sum (principal) borrowed.

Compound Interest (C.I.)

Money is said to be lent at compound interest when at the end of a year or other fixed period, the interest that has become due is not paid to the lender, but is added to the sum lent, and the amount thus obtained becomes the principal for the next year or period. The process is repeated until the amount for the last period has been found. The difference between final amount and the original principal is the compound interest (C.I.)

In compound interest, interest is calculated on the accrued interest also.

Amount = P[1+R/100]^N

Compound Interest = Amount – Principle

Note:

The time period after which the interest is added each time to form a new principal is called conversion period. It may be annually, semi-annually or quarterly.
In case, interest is paid semi-annually (half yearly), N is number of half years and R is rate percent per half year i.e., Number of years x 2 = Number of half years. Rate percent per annum x 2 = Rate percent per half year.
In case interest is paid quarterly, N is number of quarters and R is rate percent per quarter. Number of years x 4 = Number of quarters Rate percent per quarter + 4 = Rate percent per quarter.
When rates are different for different years, say R₁, R₂, R₃ percent of 1st, 2nd and 3rd years respectively then Amount = P[1+R₁/100][1+R₂/100][1+R₃/100]

Hire Purchase

In a hire purchase plan, a customer can make use of the goods while paying for them. The amount paid at the time of purchase is called down payment. The remainder is paid in equal instalments and each is the monthly instalment. The difference between total amount to be paid and the cash price is called instalment charge. Monthly Instalment = [Amount to be paid – down payment]/Number of instalments

PROFIT AND LOSS

Cost Price (CP): The price for which an article is bought is called its cost price.
Selling Price (SP): The price at which an article is sold is called its selling price.
Profit (Gain): The difference between selling price and cost price is called profit. For profit, selling price should be greater than cost price.
Loss: The difference between cost price and the selling price is called loss. When cost price is greater than the selling price, there is a loss. Profit and loss is generally represented as a percent of the cost price, unless otherwise stated.

Overhead charges: If an individual has to spend some money on transportation etc ., then this extra expenditure is called overhead charges.
Marked price (MP): The price on the label is called marked price or list price.
Discount: The reduction made on the ‘marked price’ of an article is called discount. When no discount is given, ‘selling price’ is the same as ‘marked price’.

PARTNERSHIP

It is an association of two or more persons who invest their money in order to carry on a certain business. A partner who manages the business is called working partner and the one who simply invests the money is called sleeping partner.

If capitals of the partners are invested for the same time, then partnership is called simple, and if invested for different periods, the partner is called compound. If period of investment is the same for each partner, then profit or loss is divided in the ratio of their investments.

Monthly Equivalent Investment

It is the product of the capital invested and the period for which it is invested. If period of investment is different, then profit or loss is divided in the ratio of their Monthly Equivalent Investment.

STOCKS AND SHARES

Face value: The price of a share is printed on the share certificate is called face value of the share. (Nominal value).
Dividend: Every shareholder of a company is entitled to a proportionate share of the profits of the company. The amount of profits on each share is called dividend. Dividend is expressed as a percentage of the face value.
Market Value: In the market, selling price of the share may be different from its face value. Thus, market value of a share is fluctuating price.
Shares: In the market, three types of shares are available

Premium share: If market price of a share is more than nominal value, then it is called premium share.

Par share: If market price of a share is equal to the nominal value, then it is called par share.

Discount share: If market price of a share is less than the nominal value, then it is called a discount share.

Types of Shares

Preference shares: On these shares a fixed rate of dividend is paid to share holders irrespective of whether the company makes any profits or whether it runs into loss. In case the company is not able to pay the agreed dividend to preference shareholders, the dividend on cumulative preference shares goes on accumulating and is paid as and when the company can do so.
Equity shares: Profit of the company that is left over after its distribution to the preference shareholders is distributed among the equity share holders. This dividend on equity share may sometimes be more or sometimes less than the dividend on the preference share.

Stock

In order to meet expenses of a certain plan, the Government of India sometimes raises a load from the public at a certain fixed rate of interest. Bonds or promissory notes called stocks of a fixed value are used for sale to the public.