**Time Value of Money**

**Time Value of Money** states that dollar today is worth more than will tomorrow. Because Inflation (Persistent rise in the general price level over a period of time) and Opportunity Cost (The cost of next best alternative forgone):

## The Interest

Fee paid on borrowed money. Compensation to lender for foregoing other useful investment. Equilibrium price at which demand and supply of fund meet

I = Interest (The charge for the privilege of borrowing money, typically expressed as an annual percentage rate APR)

RR = Real Rate (An absolutely risk-free investment over a specified period of time)

IF = Inflation Factor (The rate at which the general level of prices for goods and services is rising)

DR = Default Risk (Default risks that companies or individuals will be unable to make the required payments on their debt obligations)

MR = Maturity Risk (Risk associated with interest rate uncertainty. The longer the time to maturity, the higher the premium)

## Types of Interest

It is cost to borrow money. The rent one pays for the use of money is called the interest**. **There are three types of interest

### Simple Interest

- Interest calculated on principal amount only
- Although the interest rate is often specified for a year, it may be specified for a week, a month, or a quarter, etc.

SI_{n }= Simple Interest for n time period P = Principal Amount

i = Rate of Interest n = Time period

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** Illustration 1:** Mr. Salman has three options for investment. Option first offered by Allied Bank is deposit Rs. 100 in a five-year certificate of deposit paying 10% simple interest. How much will have at the end of the five-year?

### Discrete Compound Interest

Interest on principal as well as on interest is called compound interest

CI_{n }= Compound Interest for n time period P = Principal Amount

i = Rate of Interest n = Time period

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** Illustration 2:** Mr. Salman has second option offered by National Bank is deposit Rs. 100 in a five-year certificate of deposit paying 10% discrete compound interest. How much will have at the end of the five-year? Find out the difference of interest between compound and simple interest?

Difference of Interest = Compound interest – Simple Interest

Difference of Interest = 161.05 – 150 = Rs. 11.05

This mean interest on principal is Rs. 50 and interest on interest is Rs. 11.05

### Continuous (Exponential) Compound Interest

- As name suggested that it has exponential increase rate of interest
- When interest is compounded “many times”, we say that the interest is compounded continuously

** Illustration 3:** Last option having by Mr. Salman which offered by United Bank is deposit Rs. 100 in a five-year certificate of deposit paying 10% continuous compound interest. How much will have at the end of the five-year? Which is best choice?

## Types of Interest Rates

There are three types of interest are generally used

### Fixed Interest Rates

Stated and unchanged rate of interests

### Floating / Market Interest Rates

Fluctuating rate of interest based on market conditions

### Combined / Dictated Interest Rates

Mix of fixed and floating rate of interests

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## Investment Evaluation by Time Value of Money

There are two Time Value of Money techniques are used to evaluate investments