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1. Mathematics
of Finance
Presented To:
Professor Dr. Md. Showkat Ali
Chairman
Department of Applied Mathematics
University of Dhaka
Presented By:
Md. Mehedi Hasan
ID- 019
Section – A(24)
MBA Professionals 1

2. Introduction
Mathematical finance, also known as quantitative finance and financial
mathematics, is a field of applied mathematics related to the
mathematical modeling of financial markets.

3. Objectives
• To know the interest.
• To know the simple interest and compound interest.
• To solve the problems of Simple Interest and Compound Interest.
• Applying compound interest and simple interest formula to calculate the
future value of an investment or loan.
• Recognize the knowledge of simple and compound interest in real-life
situations like choosing a better investment/loan offer.

4. Interest
Financial interest is the payment from a borrower or financial institution
that receives a deposit to a lender or depositor greater than the
repayment of the principal at a given rate. This is different from the fees
that the borrower can pay to the lender or to a third party. There are two
types of interest, one is simple interest and the other is compound
interest

5. Simple Interest
Simple interest is interest calculated on the principal portion of a loan or
the original contribution to a savings account.
Formula
F = P + P*i*n
= P(1+in)
Where,
F= Future value
P= present value
i= Interest rate
n= Time in years

6. Example
Stephen invested $300 on an account that pays 10% simple interest. How
much will his investment be worth after 3 years?
Solution
Here,
P= $300, i= 10% or 0.1, n= 3 years
F=?
We know,
F = P(1+in)
= 300 {1+ (0.1)3}
= 390
Therefore his investment will be worth $390 after 3 years.

7. Compound Interest
At the end of the payment period, if interest and initial capital earn another
interest during the next payment period and are reinvested at the same rate,
the interest paid on the reinvested interest is called compound interest.
Formula
F= P(1+i)n
Where,
P= Present value
F= Future value
m= Number of a compounding period per year
i= r/m= Rate of interest Per period
n= Total number of period

8. Example
How long will it take for $10,000 to grow to $25,000 if it invested at 18%
compounded quarterly?
Solution
Here,
P= $10,000, F= $25,000, m= 4 for Quarterly
r= 18% or 0.18
i= r /m= 0.18= 0.045
n=?

9. We know,
F= P(1+i)n & if calculate Years= Period/m
=> 25,000=10,000(1+0.045)n
=>2.5=(1.045)n
=>log2.5= log(1.045)n
=>log2.5= n log 1.045
=>log 2.5/ log 1.045=n
=>n= 20.8168 period
=>n= 20.8168/4
=>n= 5.21 Years
So, it will take 5.21 Years.