Financial Mathematics is an important subject and knowledge of it enhances a person's reasoning and problem-solving skills.

1. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Affiliated to Institution of G.G.S.IP.U, Delhi
FINANCIAL MATHEMATICS
(18105)
Kanika Sharma
Assistant Professor

2. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
SCOPE OF FINANCIAL MATHEMATICS
• Financial Mathematics is an important subject
and knowledge of it enhances a person's
reasoning and problem-solving skills.
• It has a real life application in theoretical and
practical problems of banking and insurance
sector.

3. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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 an
Investment
• Equation of Value involved in a Transaction
• Depreciation
• Discount

4. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
UNIT -2
• Immediate Annuity
• Deferred Annuity
• Equated Installment and the Principal and
Interest component of Individual Equated
Installments
• Amortization
• Sinking Fund Operations
• Preparation and use of Interest Table

5. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

6. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
UNIT-4
• Computation of Mathematical Premium in life
Insurance Business
• Tenure of Life Insurance Contract
• Theory of Credibility
• Application to Rate making in Non-Life
Insurance Business
• Application of Equation of payment for
Determining the Mathematical Premium

7. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

8. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
TYPES OF INTEREST
• Simple Interest: Interest paid(earned) on only
the original amount borrowed (lend)
• Compound Interest: Interest paid(earned) on
any previous interest earned , as well as on
the principal borrowed (lend)

9. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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)

10. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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?

11. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

12. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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)

13. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
NOMINAL AND EFFECTIVE RATE OF
INTEREST
Nominal rate of interest : The stated annual rate
of interest is called nominal rate of interest
Effective rate of interest: The actual percentage
by which the money grows during a year is
called effective rate of interest

14. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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 is
A = 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

15. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

16. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

17. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

18. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
DEPRECIATION
The decrease in the value of an asset, which
cannot be made by current repairs is called
depreciation.
The value of depreciable assets at the end of its
useful life is called the scrap value

19. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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

20. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 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 for
Management , McGraw Hill Education
• A . Lenin Jothi, Financial Mathematics,
Himalaya Publishing House

21. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75