# Time Value of Money: The Underlying Concepts

You may have heard the metaphor “Time is money,” but did you ever give this metaphor any serious thought? The Time Value of Money (TVOM) is the value of money that would be in the future, when a certain time is elapsed since you made an investment or you lend the money to someone. So when you come to think of it, we started from the barter system, then we jumped into currencies, and from there we go from hundreds to thousands to lakhs; and then further on to billions. How did that happen? A certain commodity only costs $10, 5 years back and now the same commodity costs $100. What is bringing about this change?

The change is inflation, as the economy of a country grows, things get costlier and the value of a certain amount of money decreases with the passage of time. Calculation of TVOM problems can be made with the help of simple or advanced math skills, as you can find in this course.

If you want to understand this in simple terms, you should understand that the value of money is ever increasing. Ten dollars five years back is equivalent to six dollars today. Hence, the time value of money decreases every year. Thus, if you want to recover ten dollars that you lend to someone 5 years back, you need to take some interest on it in order to be protected from loss. Let’s understand this with an example:

Suppose your friend asks you to lend him 5000 dollars for 3 years that he needs to start his business. If you choose to keep those 5000 dollars with you, then you could invest it in a bank or buy some gold that may keep increasing its value with time. But when you choose to give it to a friend you receive no such benefit from it. Thus, after 3 years you should not take back $5000 from him, you should always take more some money than that. Time value of money deals with this ‘extra money’ that you should take from the debtor in order to compensate for the loss that incurred due the decrease in the value of the money that you had lent for the period.

TVOM is a classic problem in economics and a number of methods have been devised for its calculation depending on various scenarios. TVOM forms the basis of almost all transactions involving money lending and financing. To learn more about finance and financial modeling, check out this course.

**Time Line **

Time line is a visual tool that helps analyze the Time Value of Money Problem. It is nothing but a straight line that shows some parameters populated on it. The three parameters are:

- Time Period
- Interest Rate
- Cash Flow

Time period is the interval of time populated on the time line. A time period could be a time interval of any duration such as: a year, 2 years, 3 years, etc. Interest rate is the % of money earned in a particular time period. Cash flow is the amount of money that is present in a particular year. The unknowns in a time line calculation could be any one of the three parameters.

## Present and Future Value

The present value of the money is the amount of money that you have in the present and the future value is the amount of money that you should have in the future considering money growth trends. In a time line, the present value is the value of money at the beginning of the timeline and future value is the value of the money in the future, populated on the timeline.

## Simple and Compound Interest Rates

While solving a Time Value of Money problem one may come across simple and compound interest calculations. To successfully solve such problems one needs to know what they actually mean.

Simple interest is a percentage of the principal money calculated for a particular time period. The simple interest is always calculated on the initial principal amount. For example, suppose you want to calculate the simple interest on a principal amount of Rs. 1,00,000 for an interest rate of 2% for 2 years. The simple calculation would be:

Simple Interest = Principal * Rate * Time / 100 = 100000*2*2/100 = 4000.

But, when you want to calculate the compound interest on the same amount, you may want to know how much the value of the money has increased in one year, suppose it comes out to be x. Then, you calculate interest on that amount x plus the principle amount, for one year, and so on. So in compound interest the principal keeps on changing per time period specified. Simple interest is not a very complex topic and with a simple tutorial one may get a hang of the topic.

## Types of TVOM

There are seven different types of TVOM. They are:

**Lump Sum:**In the lump sum TVOM calculation one does not consider any intermediate value between the PV and FV. The calculation is simple and the future value is calculated with the simple formula:

*Future Value = Present Value *(1+rate) ^{time}*

**Multiple Cash Flows:**In this type of TVOM problem, there are many cash flows in between the time lines. Hence the calculation of FV becomes a little complicated.**Annuity:**If the multiple cash flows in between the time lines is a constant and comes at a constant time period, then it becomes a problem of annuity.**Annuity Due:**It is very much like annuity, but the constant payment stops before the last time period. That is one payment short, thus the name Annuity Due.**Perpetuity:**It is almost like annuity with the constant payments continuing for an infinite amount of time**Growing Perpetuity:**Almost the same as perpetuity, in growing perpetuity the constant payment keeps increasing by a specified rate indefinitely.**Growing Annuity:**In this, the constant payment keeps increasing by a specified rate but only up to particular time limit.

All these TVOM problems can be solved with the help of a time line and mathematical calculations. Use this excellent tutorial on TVOM for some practice questions. Also, read more on finance and related topics to become a Chartered Financial Associate.

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