Time Value of Money

What is The Time Value of Money?

Time Value of Money Definition

The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. 
A dollar on hand today is worth more than a dollar to be received in the future because the dollar on hand today can be invested to earn interest to yield more than a dollar in the future. The Time Value of Money mathematics quantify the value of a dollar through time. This, of course, depends upon the rate of return or interest rate which can be earned on the investment.
The Time Value of Money has applications in many areas of Corporate Finance including Capital Budgeting, Bond Valuation, and Stock Valuation. For example, a bond typically pays interest periodically until maturity at which time the face value of the bond is also repaid. The value of the bond today, thus, depends upon what these future cash flows are worth in today's dollars.
The Time Value of Money concepts will be grouped into two areas: Future Value and Present Value. Future Value describes the process of finding what an investment today will grow to in the future. Present Value describes the process of determining what a cash flow to be received in the future is worth in today's dollars.

How to Calculate Time Value of Money

1.Choose an option. If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth, compared to Option B? Let's take a look,by following given below solved examples..

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If you chose Option A and invest the total amount at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450, which of course is calculated by multiplying the principal amount of $10,000 by the interest rate of 4.5% and then adding the interest gained to the principal amount:

• Future value of investment at end of first year:
  • = ($10,000 x 0.045) + $10,000
    • = $10,450

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You can also calculate the total amount of a one-year investment with a simple manipulation of the above equation:

• Original equation: ($10,000 x 0.045) + $10,000 = $10,450
  • Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450
    • Final equation: $10,000 x (0.045 + 1) = $10,450

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The manipulated equation above is simply a removal of the like-variable $10,000 (the principal amount) by dividing the entire original equation by $10,000.

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What is Probability, Definition And More

What is Probability?
Probability Definition: Chances of occurring an event is known as  Probability.
Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty: for example, the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat. An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5, because the toss is equally as likely to result in "tails." An event with a probability of 0 can be considered an impossibility:
Probability Examples, the probability that the coin will land (flat) without either side facing up is 0, because either "heads" or "tails" must be facing up. A little paradoxical, probability theory applies precise calculations to quantify uncertain measures of random events.
In its simplest form, probability can be expressed mathematically as: the number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes):
Probability Formulas

p(a) = p(a)/[p(a) + p(b)]

Calculating probabilities in a situation like a coin toss is straightforward, because the outcomes are mutually exclusive: either one event or the other must occur. Each coin toss is an independent event; the outcome of one trial has no effect on subsequent ones.

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Normal Distribution

Normal Distribution

Normal Distribution Definition

 The normal distributions are a very important class of statistical distributions. All normal distributions are symmetric and have bell-shaped density curves with a single peak. A function that represents the distribution of many random variables as a symmetrical bell-shaped graph.

A normal distribution in a variate with mean and variance is a statistic distribution with probability density function

(1)

on the domain . While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell curve." Feller (1968) uses the symbol for in the above equation, but then switches to in Feller (1971).
de Moivre developed the normal distribution as an approximation to the binomial distribution, and it was subsequently used by Laplace in 1783 to study measurement errors and by Gauss in 1809 in the analysis of astronomical data (Havil 2003, p. 157).

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