1. UNIT
Percentage
F.Y.B.Com
Prof.P.A.Navale
Dept. of Commerce

2. Percentage
Percentage is a mathematical concept that appears very frequently in everyday life. You read that a merchant is offering a twenty percent discount on a selected group of items.
The manufacturer of an article of clothing states that the material is sixty-five percent Dacron and thirty five percent polyester.
A) The Meaning of Percent:
Percent is a term derived from two Latin words per centum which mean by the hundred. The symbol for percent is i.e. observing this symbol carefully, one notices that it contains the numerals which represent the number one hundred. Percent means hundredths. One hundred hundredths equal one whole item. If a percent is less than 100% it is equivalent to a fraction less than one. If a percent is more than 100% it is equivalent to a fraction greater than one.

3. Percentage B) Computing Percentages:
To compute a percentage of a specific number. follow the steps below:
a) Change the percent to the decimal form.
b) Multiply the decimal form times the specific number.
c) Count all places to the right of the decimal points in the problem.
d) Place the decimal the same number of places to the right of the decimal in the answer.
Case 1) :Percentages less than 100:
Example: 30% of 80 = 80 X .30 = 24.00
Answer: 30% of 80 = 24
Case 2) : Percentages greater than 100:
Example: 200% of 75 = 75 X 2.00 = 150
Answer: 200% of 75 = 150.

4. Percentage C) Some Formulas in Percentage: 1) Percentage Change:
% change = new value - original value × 100
                            Original value
2) Percentage Error
% error =  Error × 100
           Real value
3) Percentage Increases and Interest
New value = 100 + percentage increase × original value
                            100
4) Compound Interest:
(100 + %change)no of years × original value
5) Percentage decreases
New value = 100 - percentage decrease × original value
                              

5. Percentage D) Computing percentage of following:
1) Sales tax and Gratuities:
Sales tax is levied on the sale of a commodity, which is produced or imported and sold for the first time. If the product is sold subsequently without being processed further, it is exempt from sales tax.
Example:
Mary bought a purse for Rs. 100and a pair of shoes for Rs What total amount did she pay if a 7.5% sales tax was added to the price of the items?
Solution:
Rs. l00 + Rs. 190 = Rs. 290
7.5/100 x 290/1= Rs Sales Tax
Rs Rs = Rs Total Paid
So, Mary has to paid Rs. Totally.

6. Percentage 2) Discount:
A good way to save money is to shop when merchandise is on sale. After Christmas many stores reduce the prices of toys, furniture, and other household items. In late February and March winter clothing usually is cleared out at lowered prices. Following the fourth of July there are reductions on summer items.
Example:
Janet bought a coat which usually sells for Rs at 25% off. What did she pay for the coat?
Solution:
  25/100 x Rs = 1/4 x
= Rs
Rs Rs. 245 =Rs
So, Janet paid Rs for the coat.

7. Percentage 3) Commission:
Manufacturers and producers of goods are not always able to sell their own products. It is necessary for them to employ agents to sell the articles for them. The pay received by the agent, or salesman, for work or services performed is called commission. Sometimes the commission is a certain amount for each article sold. Sometimes the commission is a certain amount for each article sold. Other times it is a percentage of the dollar value of the sales.
Example:
A salesman who works on a commission basis receives 12% of his sales. How much was his commission on a sale amounting to Rs. 2650?
Solution: 
Let N= the missing number.
Change 12% to 12/100.
12/100 x 2650/1= N
31800/100= N
N = Rs
The salesman earned Rs commission.

8. Percentage 4) Simple interest:
Just as people pay for the use of items belonging to others, they pay for the use of money belonging to someone else. The price paid for the use of money is called interest. Simple interest is the amount paid on a sum of money, borrowed or invested, which remains unchanged for a specific period of time.
Example:
Steve borrowed Rs at 14% per year simple interest for 8 months. What was the total amount due when he repaid the loan?
Solution:
Principal = Rs Rate of Interest = 14/100
Time = 8/12 year
Interest = Principal x Rate x Time
Interest = Rs /1 x 14/100 x 8/12
= Rs
Amount Due = Principal + Interest
Amount Due = Rs Rs = Rs

9. Percentage 5) Compound Interest:
Simple interest is computed on a principal which remains unchanged for a specific period of time. Compound interest is calculated on a principal that changes at the end of stated time period when interest is added to it. The time period may be any interval during the year such as annually, semi-annually, quarterly, monthly or daily.
Example:
John invested Rs. 500 at 6% compounded monthly. How much compound interest did he earn during the tour months?
Solution:

10. THANK YOU