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: Insurance
Insurance is a legal contract between an insurance company (insurer) and a person covered by the insurance (insured), which creates security or monetary protection against possible damage or loss.
Definition: Fire Insurance
Fire insurance is property insurance that covers damage and losses caused by fire to property like buildings, godowns
containing goods, factories, etc.
Definition: Marine Insurance
Insurance that covers goods or cargo against loss or damage during transit by sea, road, rail, or air.
Definition: Accident Insurance
Insurance that provides compensation for injury, disability, death, or vehicle damage due to accidents.
Formula: Premium
Primium = Rate of Premium × Policy Value
Formula: Claim
\[\mathrm{Claim}=\mathrm{Loss}\times\frac{\text{PolicyValue}}{\text{PropertyValue}}\]
Definition: Annuity
An annuity is a series of payments at fixed intervals, guaranteed for a fixed number of years or the lifetime of one or more individuals.
Key Points: Annuity
Phase:
| Phase | Meaning |
|---|---|
| Accumulation Phase | Period during which money is invested/deposited. |
| Distribution Phase | Period during which payments are received. |
Types of Annuities:
| Type | Meaning |
|---|---|
| Annuity Certain | Payments for a fixed number of years. |
| Contingent Annuity | Payments depend on an event (e.g., death). |
| Perpetual Annuity (Perpetuity) | Payments continue forever. |
Classification of Annuities:
| Type | Payment Time |
|---|---|
| Immediate (Ordinary) Annuity | Payment at the end of each period. |
| Annuity Due | Payment at the beginning of each period. |
| Deferred Annuity | Payment starts after a certain period. |
Formula: Immediate Annuity
Amount of accumulated (future) Value:
\[P^{\prime}=\frac{C(1+i)}{i}[1-(1+i)^{-n}]\]
Present value P:
\[:P=\frac{C}{i}[1-(1+i)^{-n}]\]
Formula: Annuity Due
Accumulated (Future) Value:
\[A^{\prime}=\frac{C(1+i)}{i}[(1+i)^n-1]\]
Present Value:
\[P^{\prime}=\frac{C(1+i)}{i}[1-(1+i)^{-n}]\]
Formula: Relation between Future Value and Present Value
\[A=P(1+i)^n\]
