# Mathematical Finance

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# Mathematical Finance

Introduction

Mathematical finance is a branch of applied mathematics. Mathematical finance is also known as quantitative finance. It has a prominent use in many different parts of economics, especially in banking. Financial Mathematics includes a whole range of problems related to calculating the final value of capital. Capital is the value (in the form of money, property or human resources), which is invested in the production or other economic activity with the main purpose to increase value or to make a profit.  The capital can be invested in the production or non-production sector. Its main purpose, however, is always the same, and that is the increasing basic value or the production of other goods.

With mathematical finance it is possible to answer the following questions:

Is it better to buy a good today or tomorrow?

Should I invest money in the bank?

Do my earnings in dollars convert into foreign currency?

Would it be financially wiser to acquire a new car for cash, credit or a lease?

What are the best securities in which to invest money?

When is it advisable to take a bank loan?

Importance of Mathematical Finance

In terms of limited financial resources, it is necessary to make the wisest decision about where to invest. With the help of mathematical finance, it is possible to increase the profitability of a company.  It involves making the right decisions at the right time. Once the wrong decision has been made, it is very difficult to put the company back on the right path. This can make a tremendous difference in the following areas:

2. Banks, insurers, and other financial institutions
3. Legislation
4. Litigation
5. Education of staff and citizens

Simple and Compound Interest Calculation

Simple and compound interest are the most common methods of calculation interest.

The General definition for interest is the fee for using borrowed money. It can be explained as an expense for the person who borrows money and income for the person who lends money. Interest can be charged on principal amount at a certain rate for a certain period. For instance, 12% per year, 3% per quarter or 1% per month etc.

By definition, the principal amount means the amount of money that is originally borrowed from an individual or a financial institution and it does not include interest. In real life, the interest is charged using one of two methods- simple or compound calculation.

Simple Interest (Is) = P × i × t

Where,

P is the principle amount;

i represents the interest rate per period;

t is the time for which the money is borrowed or lent.

Compound Interest (Ic) = P × (1 + i) n – P

Where,

P is the principle amount;

i represents the compound interest rate per period;

n refers to the number of periods.

References:

• An Introduction to Quantitative Finance, Stephen Blyth
• Quantitative Methods for Business, David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
• Quantitative Methods for Finance, Terry Watsham (Author), Keith Parramore

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