Topics
Mathematical Logic
Matrices
Differentiation
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative
- Overview of Differentiation
Applications of Derivatives
Integration
Definite Integration
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
- Overview of Application of Definite Integration
Differential Equation and Applications
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
- Overview of Differential Equations
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Concept of Discount
- Overview of Commission, Brokerage and Discount
Insurance and Annuity
- Insurance
- Types of Insurance
- Annuity
- Overview of Insurance and Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
- Overview: Linear Regression
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
- Overview of Time Series
Index Numbers
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Overview of Index Numbers
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem
- Overview of Linear Programming
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
- Overview of Assignment Problem and Sequencing
Probability Distributions
- Poisson Distribution
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
- Overview of Binomial Distribution
Definition: Agent
A person who buys/sells goods on behalf of another person is called an agent.
Definition: Principal
Principal refers to an individual party or parties participating in a transaction.
or
The person who appoints the agent.
Definition: Commission
The charges paid to an agent for doing the work on behalf of the principal are called commission.
Definition: Broker
A broker is an agent who brings together the buyer and the seller for the purpose of purchase or sale. This commission is called brokerage and is charged to both parties.
Definition: Auctioneer
An auctioneer is an agent who sells goods by auction. He sells goods to the highest bidder.
Many a time name of the principal is not disclosed in the transaction.
Definition: Del Credere Agent
A del credere agent gives a guarantee to his principal that the party to whom he/she sells the goods will pay the sale price of the goods.
Formula: Commission
\[\textbf{Commission}=\frac{\mathrm{Rate}}{100}\times\mathrm{Sales}\]
Seller’s Amount = Sales − Commission
Formula: Total Commission
Definition: Trade Discount
Trade discount is allowed by one trader to another. It is given on the catalogue price, list price or market price of the goods.
Definition: Cash Discount
Cash discount is a reduction in the invoice price allowed by the seller to the buyer for making immediate or prompt payment. It is calculated on the amount remaining after deducting the trade discount from the list (catalogue) price.
Formula: Invoice Price
Invoice price = List price (Catalogue price) – Trade discount.
Formula: Net Selling Price
Selling Price / Net Selling Price = Invoice price – Cash discount
Formula: Profit
Profit = Net selling price – Cost price
Formula: Loss
Loss = Cost price – Net selling price
Definition: Present Worth (P.W.)
Present Worth is the amount payable today, which is equivalent to a larger amount due in the future at a given rate of interest.
Definition: Sum Due (S.D.) / Face Value (F.V.)
Sum Due is the total amount payable at a future date. It includes the present worth plus the interest for the given period.
Definition: True Discount (T.D.)
True Discount is the interest on the present worth at a given rate of interest for a given period.
Formula: Relationship between Present Worth, Sum Due and True Discount
Present Worth + True Discount = Sum Due
i.e.,
P.W. + T.D. = S.D.
Formula: True Discount
\[\mathbf{T.D.}=\frac{P.W.\times n\times r}{100}\]
Definition: Drawer and Drawee
A person who draws the bill is called the Drawer. A person on whom the bill is drawn is called the Drawee.
Definition: Date of Bill
The date on which the bill is drawn is called the Date of Bill.
Definition: Nominal Due Date and Legal Due Date
Nominal Due Date:
The date on which the period of the bill expires is called the Nominal Due Date.
Legal Due Date:
The date obtained after adding 3 days of grace to the nominal due date is called the Legal Due Date.
Definition: Discounting a Bill
When the drawer wants money before the legal due date, the bank deducts some amount from the face value and pays the remaining amount to the drawer. This process is called Discounting of a Bill.
Definition: Banker’s Discount
The amount deducted by the bank from the face value of the bill at a given rate of interest for the period from the date of discounting to the legal due date is called Banker’s Discount.
Definition: Cash Value
The amount paid to the holder of the bill after deducting banker’s discount is called the Cash Value of the bill.
Definition: Banker’s Gain
The difference between the banker’s discount and the true discount is called Banker’s Gain. It is equal to the interest on the true discount.
Formula: Banker’s Discount
\[\mathbf{B.D.}=\frac{S.D.\times n\times r}{100}\]
Formula: Banker’s Gain
OR
\[\mathbf{B.G.}=\frac{T.D.\times n\times r}{100}\]
Formula: Cash Value
C.V. = S.D.− B.D.
