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_ The Time Value of Money
by Carl Marx of http://financialsupport.weebly.com
Introduction
Would you rather have $ 1,000-00 today or $ 1,000 in 5 years? If you are like most people the obvious answer is to want the $ 1,000-00 today. The truth is five years is a long time to wait. During the five years a lot of things can go wrong and you may never see the $ 1,000-00. Why would any reasonable individual postpone receiving money to the future when he or she could have the same amount of money now? For the majority of people, having the money now is just common sense.
This is understandable as any money you receive today can be used to fund investment or for consumption purposes immediately. This implies that the sooner one receives money the sooner it can be put to work. This concept is referred to as the Time Value of Money!
The question clearly is why focus on time when money is involved. Well, time affords one the opportunity to immediately start earning interest on the money. Not having the opportunity to earn interest on money is generally called the opportunity cost.
Comparing Amounts at Different Times
The question that inevitably comes to mind is how one can compare amounts at different time periods. It should be clear that one cannot compare the value of money that is available at different times without adjusting the values for the various durations.
The primary factor that influences the value of the adjustment is the risk associated with waiting for the money. This risk is expressed as an interest rate.
To determine the value of money at different times one can use an interest rate that reflects the risk associated with the situation and time. The interest rate is often defined to the price of money. It may be useful to remember that the interest rate is normally expressed as a percentage of the principal value.
Simplifying the concept, the amount charged by a lender to a borrower for the use of assets, typically for a period of one year, divided by the principle value of the assets expressed as a percentage is known as the annual rate percentage.
In other words the interest rate is the rate which is charged, paid or sacrificed for the use of money or asset for the given time period. In the next section the various concepts will be explained further.
Present Value
In order to further clarify the concept one needs to understand a few critical terms. The first of these is "Present Value". If one receives the $ 1,000-00 today, the present value would of course be $ 1,000-00, because the value of the amount at present is what you receive today.
Interest rates often change as a result of inflation and other associated risks. For example, if a lender charges a lender $ 90-00 in a year on a loan of $ 1000-00, then the interest rate would be [(90÷1000)X(100÷1)] = 9%.
In other words If $ 1000-00 is deposited in a savings account that pays 9% interest annually, with interest paid at the end of the year, then at the end of the year, $ 90-00 of interest will be added to the $ 1000-00 principal amount resulting in a total of $1090-00 in your hand.
This can be expressed as an equation as follows. If the principal amount is represented as a P and the interest rate per year is expressed as i, then the amount of money available at the end of the year can be expressed by the equation P x (1 + i).
Future Value
If the $ 1,000-00 were only received in one year's time, the present value of the amount would not be $ 1,000-00 because you do not have it in your hand today. That implies that some amounts will be expressed as a "Future Value". The future value can be defined as the total value of an amount you will receive at the end of the period. In order to determine the present value of the $ 1,000-00 you will receive at the end on the year, you need to treat the $ 1,000-00 as the future value. To compare the $ 1000-00 received today with the same amount received in one year one needs to find the present value of the future $ 1,000-00. Another way to look at it is to calculate how much you would have to invest today in order to receive the $ 1,000-00 in one year form today. This process is called discounting.
Discounting
Discounting is the process of determining the present value of future value. This is the reverse of determining the future value of a payment, as in this instance the future value is already known. The present value is calculated by dividing the future value by the interest factor. The interest factor is reflected by the expression (1 + i) n, where i is the annual interest rate expressed as a decimal and n is the number of years.
There are three factors that govern the present value of a future value. The first one is the size of the future value. Is should be obvious that the larger the future value, the larger the present value.
The second one is the risk associated with receiving the future value. As uncertainty of receiving the future value increases, the expectation to receive a future certain value decreases which decreases the value that should be paid today for that future value. The risk is expressed as the interest rate.
The third factor is the time period that will have to be waited to receive the future value. The longer one has to wait, the less value the future value will have. The duration reduces the present value of a future value more and more as the time increases as uncertainty increases into the future.
Conclusion
The basic idea behind the time value of money is that money has different values depending on when it is received. The risk assassinated with whether or not money will be received in the future will influence the value of the proceeds.
The concepts associated with the time value of money has a lot of practical applications and can be of significant value in determining the best investment to make.
© Carl Marx 2009
by Carl Marx of http://financialsupport.weebly.com
Introduction
Would you rather have $ 1,000-00 today or $ 1,000 in 5 years? If you are like most people the obvious answer is to want the $ 1,000-00 today. The truth is five years is a long time to wait. During the five years a lot of things can go wrong and you may never see the $ 1,000-00. Why would any reasonable individual postpone receiving money to the future when he or she could have the same amount of money now? For the majority of people, having the money now is just common sense.
This is understandable as any money you receive today can be used to fund investment or for consumption purposes immediately. This implies that the sooner one receives money the sooner it can be put to work. This concept is referred to as the Time Value of Money!
The question clearly is why focus on time when money is involved. Well, time affords one the opportunity to immediately start earning interest on the money. Not having the opportunity to earn interest on money is generally called the opportunity cost.
Comparing Amounts at Different Times
The question that inevitably comes to mind is how one can compare amounts at different time periods. It should be clear that one cannot compare the value of money that is available at different times without adjusting the values for the various durations.
The primary factor that influences the value of the adjustment is the risk associated with waiting for the money. This risk is expressed as an interest rate.
To determine the value of money at different times one can use an interest rate that reflects the risk associated with the situation and time. The interest rate is often defined to the price of money. It may be useful to remember that the interest rate is normally expressed as a percentage of the principal value.
Simplifying the concept, the amount charged by a lender to a borrower for the use of assets, typically for a period of one year, divided by the principle value of the assets expressed as a percentage is known as the annual rate percentage.
In other words the interest rate is the rate which is charged, paid or sacrificed for the use of money or asset for the given time period. In the next section the various concepts will be explained further.
Present Value
In order to further clarify the concept one needs to understand a few critical terms. The first of these is "Present Value". If one receives the $ 1,000-00 today, the present value would of course be $ 1,000-00, because the value of the amount at present is what you receive today.
Interest rates often change as a result of inflation and other associated risks. For example, if a lender charges a lender $ 90-00 in a year on a loan of $ 1000-00, then the interest rate would be [(90÷1000)X(100÷1)] = 9%.
In other words If $ 1000-00 is deposited in a savings account that pays 9% interest annually, with interest paid at the end of the year, then at the end of the year, $ 90-00 of interest will be added to the $ 1000-00 principal amount resulting in a total of $1090-00 in your hand.
This can be expressed as an equation as follows. If the principal amount is represented as a P and the interest rate per year is expressed as i, then the amount of money available at the end of the year can be expressed by the equation P x (1 + i).
Future Value
If the $ 1,000-00 were only received in one year's time, the present value of the amount would not be $ 1,000-00 because you do not have it in your hand today. That implies that some amounts will be expressed as a "Future Value". The future value can be defined as the total value of an amount you will receive at the end of the period. In order to determine the present value of the $ 1,000-00 you will receive at the end on the year, you need to treat the $ 1,000-00 as the future value. To compare the $ 1000-00 received today with the same amount received in one year one needs to find the present value of the future $ 1,000-00. Another way to look at it is to calculate how much you would have to invest today in order to receive the $ 1,000-00 in one year form today. This process is called discounting.
Discounting
Discounting is the process of determining the present value of future value. This is the reverse of determining the future value of a payment, as in this instance the future value is already known. The present value is calculated by dividing the future value by the interest factor. The interest factor is reflected by the expression (1 + i) n, where i is the annual interest rate expressed as a decimal and n is the number of years.
There are three factors that govern the present value of a future value. The first one is the size of the future value. Is should be obvious that the larger the future value, the larger the present value.
The second one is the risk associated with receiving the future value. As uncertainty of receiving the future value increases, the expectation to receive a future certain value decreases which decreases the value that should be paid today for that future value. The risk is expressed as the interest rate.
The third factor is the time period that will have to be waited to receive the future value. The longer one has to wait, the less value the future value will have. The duration reduces the present value of a future value more and more as the time increases as uncertainty increases into the future.
Conclusion
The basic idea behind the time value of money is that money has different values depending on when it is received. The risk assassinated with whether or not money will be received in the future will influence the value of the proceeds.
The concepts associated with the time value of money has a lot of practical applications and can be of significant value in determining the best investment to make.
© Carl Marx 2009
