**Theory of Interest:-** The point at which the supply and demand of capital (funds) matches is regarded as an interest rate and theory through we described the interest rate is known as theory of interest. It is actually an equilibrium price in the **Capital Market** at which the lenders and borrowers are ready to make deals with each others. The interest rate is different for each market depending on the demand and supply of capital in the market. This means that the interest rate that prevailing in the sugar market is different from the interest rate in the cotton market. But all the different interest rates are inter-related to each other within the markets of a country.

**Factors of Interest Rate – Theory of Interest**

In general Business terminology the “interest” is also known as “nominal interest”. There are certain factors of theory of interest through which the nominal interest is determined. These factors are discussed as below.

i = iRF+g+DR+MR+SR+LP

“i” is published in papers as nominal interest rate. Whereas the “real” interest rate is given as follow.

Real Interest Rate = i ̶ g

Here iRF = Risk free interest rate

g = Rate of inflation

DR = Default risk premium

MR = Maturity risk premium

SR = Sovereign risk

LP = Liquidity preference

**Risk Free Interest Rate (iRF):**

In reality there is not any single investment that can be entirely risk free. There is definitely certain amount of risk attached to all the investments and securities, because any company can become bankrupt. But in relative term, the securities issued by government are normally treated as risk free due to the reason that the chance of default of a government is very small. So the securities issued by government give the standard for the calculation of interest rates. In international environment the **US T-Bills** are generally treated as risk free whereas in Pakistan the T-Bills issued by the government of Pakistan are treated as risk free. But these Pakistani T-Bills are not entirely risk free due to the risk of sovereign risk.

**Inflation (g):**

Inflation risk is associated with every investment and security and the issuer of the security included this risk in the calculation of nominal interest rate. For example if a security of 3 years life offers 5% interest rate, and the inflation rate in the country is also 5%, then the investors are not interested in such investment. The reason is that the interest rate equalizes with the inflation rate and the investor will not receive any profit as inflation eats the wealth. So, the issuer of the security includes the inflation rate in the calculation of nominal interest rate.

**Default Risk Premium (DR):**

There is a risk associated with the every bond and share of a company in the shape of its bankruptcy or default. To compensate the risk of being default, the issuer of the bond and share add default risk premium in the nominal interest rate. There is also a possibility that a company may be unable to pay its interest payments. There is a rating agency in the USA which ranks the companies according to their debt paying ability based on their financial health. The agency ranks the good companies to bad ones as AAA, AA, A, BBB, BB, B, CCC, CC, C etc. Pakistan Credit Rating Agency (PACRA) and Vital Information Services (VIS) are the agencies that rank the securities in Pakistan.

**Maturity Risk Premium (MR):**

A security also bears some kind of risk called maturity risk. This maturity risk is related to security’s life in such a way that it can reduce the value of an investment of any specific life. For example, if an investor investing in a 5 years security may bear some risk that the interest rates may change after 1 or 2 years or the rate of inflation may change abnormally. The result will be in the shape of reduction of the value of his investment. So, the issuer of the security also add maturity risk premium in the calculation of nominal interest rate.

**Sovereign Risk Premium (SR):**

One of the current risks that almost every investor take into account is related to the default of the government due to a number of reasons like war, turmoil, trade deficits etc. This risk is especially associated with the securities issued by the government of a certain country. Devaluation, depreciation and change in the foreign exchange rates are also fall under this section. Therefore, if any investor (individual or company) is interested in investment in other countries, they analyze the economic and political conditions of that country before doing so. Due to this reason the issuer of a security compound the sovereign risk premium in the rate of nominal interest.

**Liquidity Preference (LP):**

The securities that can be easily converted into cash are liked by the investors. If a security is less liquid, then the investor wants to receive some kind of compensation for its sacrifice of liquidity. This in turn increases the interest rate.

**Theory of Interest – Types**

There are generally three types of theory of interest which are discussed below.

**Simple Interest (Straight Line):**

The interest that is charged only on the principal amount is called simple interest. This means that the principal amount and previous interest are treated separately. For example there is a security of 2 years, than while calculating the interest on the second year the interest of first year is not added into the principal amount. The formula of simple interest is given as below.

FV = PV + (PV x i x n)

Here FV is the future value of investment.

PV is the amount invested.

i is the interest rate that a bank offers.

n is the number of years of the investment.

**Discrete Compound Interest:**

In **financial management** discrete compound interest is mostly used in NPV calculations and Discounting. In this type of interest, both the principal as well as previous interest should be taken into account while calculating the interest for the next year. But the compounding of the interest with the principal amount happens in a discrete pattern like annually, semi-annually, quarterly and sometimes monthly. The annual compounding formula is given as follow.

FV = PV x (1 + i)^{n}

The formula of monthly compounding is as follow.

FV = PV x (1 + i/m)^{ mxn}

**Continuous Compound Interest (Exponential):**

This is a special type of compound interest in which the interest is calculated for micro second intervals of a year. In other words the interest is derived from unlimited number of times for a year. The formula of this exponential interest is

FV = PV x e^{ixn}

In the above equation “e” is constant whose value is derived as 2.718.

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