Business Mathematics plays an important role in commercial enterprises for understanding and handling everyday operations.
Commercial enterprises use Math in probability, accounting, statistics, elementary algebra, sales forecasting, inventory management, financial analysis and marketing.

Business mathematics contains a set of both mathematical and statistical tool which can be used for the fulfillment of one or more objectives of the business sector like the, maximization of profits, minimization of cost and maximization of output or sales etc.
These tools are often known as quantitative techniques.

Here are some basic definitions to understand the fundamental concepts:
Selling Price: The market price at which the product is offered for a sale is called the selling price.
Cost Price: It is the actual or original price of an item.
Profit: If the selling price of a product is more than it's cost price or original price, then we say that the product is sold at a profit.
Loss: If the selling price of a product is less than its cost price or original price, then we can say that the product is sold at a loss.
Discount: It is the deduction given on the selling price of an item.
Simple Interest: It is the interest which is paid against the principal amount alone for a given period of time and the rate of interest.
Compound Interest: It is the interest which is calculated on the accrued interest added to the principal amount over a period of time and rate of interest.

The following List of Important Formulas will help us solve all business math related problems

7) Simple interest(I) = P x T x R
Where,
I = Simple Interest
P = Principal or loan amount
T = Time period for loan taken as number of years
R = Rate of interest expressed as a decimal.
The amount to be repaid includes the interest and is therefore,
Amount = Principal + Interest

8) If "P" is the principal, "r" is the rate per annum and "n" is the number of years for which the compound interest is taken into account, then the amount (A) at the end of the nth year is given by the formula:

$A = P(1 + $$\frac{r}{100}$$)^{n}$

and Compound Interest (CI) = $A - P$

= $P(1 + $$\frac{r}{100}$$)^{n} - P)$

= $P((1 + $$\frac{r}{100}$$)^{n} - 1)$

The following problems will help us understand how to find the profit and loss values in business mathematics.

1: John purchased 240 apples at the rate of 12 dollars per apple and he sold 40% of the apples at the rate of 14 dollars per apple and the remaining apples at the rate of 12 dollars per apples. Calculate his profit percent?

Solution: Cost price of 240 apples = 12 x 240 = 2880 dollars

40% of 240 apples = $\frac{40}{100}$ x 240 apples = 96 apples

The selling price of 96 apples = 14 x 96 = 1344 dollars
and selling price of the remaining apples is 240 - 96, that is 144 apples
= 12 x 144
= 1728 dollars
So, the selling price of 240 apples = 1344 + 1728 = 3072 dollars
Profit = Selling price - Cost price
= 3072 - 2880
= 192 dollars

And profit percent = $\frac{profit}{Cost\ price}$ x 100

= $\frac{192}{2880}$ x 100

= 6.667 %
Thus john's profit percentage = 6.667%

2: The cost price of 14 pencils is equal to the selling price of 8 pencils. Calculate the profit percent?
Solution: Selling price of 8 pencils = Cost price of 14 pencils

Selling price of 4 pencils = Cost price of $\frac{14}{8}$ x 4 = 7 pencils

Profit = Cost price of 7 pencils
Investment = Cost price of 14 pencils

% profit = $\frac{7}{14}$ x 100

= 50%

3: A shopkeeper sold 2 books for 200 dollars each. On one book he gained 30% and on the other book he lost 30%, Calculate the total loss or gain for the shopkeeper?
Solution: The selling price for the first book = 200 dollars
The gain on the first book = 30%

So, Cost price = $\frac{100 \times Selling\ price}{100 + Profit}$

= $\frac{100 \times 200}{100 + 30}$

= 153.846 dollars
The Selling Price of the second book = 200 dollars
Loss on the second book = 30%

So, the Cost price = $\frac{100 \times Selling\ price}{100 - Loss%}$

= $\frac{100 \times 200}{100 - 30}$

= 285.714 dollars
Now, the total cost price = 153.846 + 285.714
= 439.56 dollars
The total selling price = 2 x 200 = 400 dollars
So, Loss = Cost price - Selling price
= 439.56 - 400
= 39.56 dollars

4: If the original price of a article is 20 dollars and it on sale for a 15% discount, then calculate the sale price of the article?
Solution: Given discount on the article = 15% of 20 dollars
To find the amount of discount

= $\frac{15}{100}$ x 20

= 0.15 x 20
= 3
Sale price of article = original price of article – discount given on the article
= 20 - 3
= 17 dollars
So, the sale price of the article is 17 dollars.

## Examples on Simple and Compound Interest

The Following Example problems will explain how to find simple and compound interest values in business mathematics.

1: John puts 550 dollars in a bank account. Each year the he earns 6% simple interest. Calculate the interest earned in 3 years?

Solution: Simple Interest = $\frac{P R T}{100}$

= $\frac{550 \times 6 \times 3}{100}$

= 99 dollars
So, John earns an interest of 99 dollars after 3 years based on 6%

2: Calculate the interest on 2570 dollars at 15% for 80 days?
Solution: Given that Principal amount(P) = 2570 dollars
Rate(r) = 15%

Time(t) = 80 days = $\frac{80}{365}$

Simple interest = $\frac{PRT}{100}$

= $\frac{2570 \times 15 \times 80}{100 \times 365}$

= 84.493 dollars

3: Calculate the compound interest and the compound amount on the amount 30,000, which is borrowed at 8% compounded for 3 years?
Solution: Given that Principal amount(P) = 30,000
Rate(R) = 8%
Time period(n) = 3 years
Compound Amount(A) = P(1 + r)^n

= 30000(1 + $\frac{8}{100}$ )3

= 37791.36
Compound interest = Compound Amount(A) - Principal amount(P)
= 37791.36 - 30,000
= 7791.36

4: Calculate the compound amount, that will be received from an interest of 4000 dollars at 5% compounded quarterly for 6 years?
Solution: Given that principal amount(P) = 4000 dollars

Rate(r) = 5% = $\frac{5}{4 \times 100}$ = 0.0125

Time period(n) = 6 x 4 = 24 quarters
Compound Amount(A) = P(1 + r)n
= 4000(1 + 0.0125)24
= 5389.40

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