TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Affiliated to Institution of G.G.S.IP.U, Delhi

FINANCIAL MATHEMATICS

(18105)

Kanika SharmaAssistant Professor

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

SCOPE OF FINANCIAL MATHEMATICS

• Financial Mathematics is an important subjectand knowledge of it enhances a person'sreasoning and problem-solving skills.

• It has a real life application in theoretical andpractical problems of banking and insurancesector.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

UNIT -1

• Rate of Interest

• Types of Interest

• Stated and Effective rate of interest

• Discounted value and Maturity value of anInvestment

• Equation of Value involved in a Transaction

• Depreciation

• Discount

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

UNIT -2

• Immediate Annuity

• Deferred Annuity

• Equated Installment and the Principal andInterest component of Individual EquatedInstallments

• Amortization

• Sinking Fund Operations

• Preparation and use of Interest Table

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

UNIT -3

• Decrement Tables

• Concept of Cohert

• Decrement and Decrement rates

• Concept of Life table

• Elements of life Table

• Double and Multiple Decrement Tables

• Elements of Service Table

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

UNIT-4

• Computation of Mathematical Premium in lifeInsurance Business

• Tenure of Life Insurance Contract

• Theory of Credibility

• Application to Rate making in Non-LifeInsurance Business

• Application of Equation of payment forDetermining the Mathematical Premium

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

INTEREST

Interest is the amount paid by the borrowers for the use of money that

they borrows from a lender

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

TYPES OF INTEREST

• Simple Interest: Interest paid(earned) on onlythe original amount borrowed (lend)

• Compound Interest: Interest paid(earned) onany previous interest earned , as well as onthe principal borrowed (lend)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

SIMPLE INTEREST

Let P be the principal at a simple rate of interest r % per annum for a period of ‘t’ years . The Interest charged at the end of t years is

SI = P × r × t

The amount at end of t years is given by :

A = P+ SI

A = P+ P. r. t

A = P(1+rt)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

EXAMPLE

QUES. What time will be required for a sum of money to double itself at 5% simple interest?

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

COMPOUND INTEREST

• Let P be the principal earning interest compounded m times a year at a rate of i per period .Let n be the number of conversion periods. Then the compound amount A is given by

A = P(1+i)n , n= m × t , i= r/m

CI = A- P

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

EXAMPLE

If Rs 1750 is invested at 9% per annum interest for 10 years and interest is compounded half yearly , find the amount and interest. (Given

(1.045)20 = 2.41)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

NOMINAL AND EFFECTIVE RATE OF INTEREST

Nominal rate of interest : The stated annual rateof interest is called nominal rate of interest

Effective rate of interest: The actual percentageby which the money grows during a year iscalled effective rate of interest

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

NOMINAL AND EFFECTIVE RATE OF INTEREST

Let Rs 100 be invested for 1 yr at 10% compounded quarterly

Here 10% is the nominal rate of interest

The amount after 1 year isA = 100 ( 1 + 0.10/4 )4 =100 ( 1.125 )4 = Rs. 110.38 Therefore the actual interest earned on Rs 100 is Rs 10.38 in 1 year

We say that the effective rate of Interest is 10.38%At 10.38% per annum rate of interest compounded annually

A= 100 ( 1 + 0.1038 ) = 100 ( 1.1038 ) = Rs. 110.38

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

RELATION BETWEEN NOMINAL AND EFFECTIVE RATE OF INTEREST

The relation between nominal and effective rate of interest is given by:-

re = ( 1+ r/m )m - 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

EXAMPLE

Find the effective rate of interest equivalent to the nominal rate 9% converted:

(a) semi-annually

(b) quarterly

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

EXAMPLE

Which is the better investment from the stand point of investor:

6.2% compounded semi annually

or

6% compounded monthly

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

DEPRECIATION

The decrease in the value of an asset, whichcannot be made by current repairs is calleddepreciation.

The value of depreciable assets at the end of its

useful life is called the scrap value

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

METHODS OF COMPUTING THE DEPRECIATION

(a) Diminishing balance Method\ Constant percentage Method\ Reducing balance Method

(b) Straight Line Method

(c) Sum of the year Digits method

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

SUGGESTED READING

• Trevedi, (2010), Business Mathematics,1st

edition, Pearson Education

• Kapoor V.K (2007), Business Mathematics ,Sultan Chand and Sons

• Raghavachari .M (2004) ,Mathematics forManagement , McGraw Hill Education

• A . Lenin Jothi, Financial Mathematics,Himalaya Publishing House

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75