# Time Value of Money

## Time Value of Money

Time value of money is the concept that an amount of money in one’s possession is worth more than that same amount of money promised in the future (Garrison, 2006). The reason for this is that money today can be invested to earn interest and therefore will be worth more in the future (Brealey, Myers, & Marcus, 2004). This paper will explain how annuities affect time value of money (TVM) problems and investment outcomes. In addition, this paper will briefly address the impact of interest rates, present value, future value, opportunity cost and the rule of 72 on the time value of money.

Interest rates are the percentage of initial investment or loan received or charged during a period of time (Brealey, Myers, & Marcus, 2004). Most interest is compound interest which is basically interest on interest (Brealey, Myers, & Marcus, 2004). For example, if someone invested $10,000 at 10% interest compounded annually he or she would receive $10,000 x 0.10 = $1000 in interest after the first year. The next year that person would have $11,000 in principle ($10,000 + $1000) earning 10% interest which would equal $1100 in interest. The third year would see $12,100 earning that 10% and so on. So interest is the multiplier that makes the fact that money has a time value a true statement.

Present value and future value are concepts that involve the affects of time on money. When calculating present value there is an assumption that a future amount of money is discounted by a certain percentage of the principle compounded for each period or year in the future (Brealey, Myers, & Marcus, 2004). The result shows how much a future amount of money is worth today. For example, if a person wanted to have $1,000,000 saved by the time they retire in 40 years, how much money do they have to invest in a lump sum today earning 10% interest? The present value = $1,000,000 divided by the interest compounded for 40 years. PV = $1,000,000/ (1.10)40 = $1,000,000/45.259 = $22,095. So $1 million 40 years from now at 10% interest has a present value of $22,095. Future value is the converse of present value in that it grows by the interest rate compounded each period for the number of years it is invested (Brealey, Myers, & Marcus, 2004). For example, a person gets a one-time gift from a rich aunt of $12,000 and invests that money in a 10-year CD at 8%. The value of that $12,000 in 10 years represents that money’s future value. FV = $12,000 x (1.08)10 = $12,000 x 2.159 = $25,907. The person has the opportunity to more than double his or her money by investing it rather than spending it today. This leads to the concept of doubling. People and investment advisors often talk about doubling their money. The rule of 72 says that the time it takes and investment to double is approximately equal to 72 divided by the interest rate expressed as a percentage (Brealey, Myers, & Marcus, 2004). For example, take the above example where a person received $12,000 from a rich aunt. How long would it take for that investment of $12,000 at 8% to double? It would take approximately 72/8 or 9 years to double in value. This formula works best with relatively low rates of interest and gives a close approximation of the length of time it take for money to double in value at a fixed interest rate (Brealey, Myers, & Marcus, 2004).

An annuity is an evenly spaced number of payments or money received in the same amount (Cedar Spring Software, Inc., 2002). Each TVM problem has five variables: interest rate or return, time or number of periods, future value, present value, and amount of payments either made or received (Brealey, Myers, & Marcus, 2004). The present value of annuity payments received over a number of years is less than if one had the full amount in hand now to invest. The reason for this is opportunity cost. If the full amount of the annuity could be invested today in a lump sum, the final value during the same term of the annuity would be much higher due to compound interest. So opportunity cost in this case is the total amount of the annuity payments over the length of the annuity and the value of investing the annuity’s total value today at a specified rate of return. For example, person is receiving annuity payments of $500 per month for 20 years will receive 12 x 500 x 20 = $120,000 during the annuity period . If that same person had $120,000 in his or her hand to invest today at a modest 6% interest compounded annually, they would have $120,000 x (1.06)20 = $384,856 at the end of the 20 years. The 0pportunity cost of this annuity is $384,856 - $120,000 = $264,856. This annuity caused the person to miss the opportunity to make an extra $264,856 over the 20-year period.

Money is more valuable when it can be invested and earn interest than if that same amount were promised in the future. The time value of money is the basis of finance and investing. The concepts that affect the time value of money are important to understand whether it be a business manager or a household manager. These ideas and concepts are so important in today’s climate of disappearing pensions, uncontrolled government spending and the likelihood that social security will not be around in 30 years. Steps should be taken to ensure that the nation’s children are taught these concepts in high school and college, so that the next generation will be prepared to manage their own financial well being.

References:

Brealey, R. A., Myers, S. C., & Marcus, A. J. (2004). Fundamentals of corporate finance (4th ed.). [University of Phoenix Custom Edition e-text]. New York, New York; McGraw Hill/ Irwin. Retrieved September 11, 2006, from University of Phoenix, Resource, FIN325 - Financial Analysis for Managers II website.

Cedar Spring Software Inc. (2002). Present value of an annuity. Retrieved September 14, 2006 from http://www.getobjects.com/Components/Finance/TVM/pva.html

Garrison, S. (2006). Time value of money. Retrieved September 14, 2006 from http://www.studyfinance.com/lessons/timevalue/index.mv

Interest rates are the percentage of initial investment or loan received or charged during a period of time (Brealey, Myers, & Marcus, 2004). Most interest is compound interest which is basically interest on interest (Brealey, Myers, & Marcus, 2004). For example, if someone invested $10,000 at 10% interest compounded annually he or she would receive $10,000 x 0.10 = $1000 in interest after the first year. The next year that person would have $11,000 in principle ($10,000 + $1000) earning 10% interest which would equal $1100 in interest. The third year would see $12,100 earning that 10% and so on. So interest is the multiplier that makes the fact that money has a time value a true statement.

Present value and future value are concepts that involve the affects of time on money. When calculating present value there is an assumption that a future amount of money is discounted by a certain percentage of the principle compounded for each period or year in the future (Brealey, Myers, & Marcus, 2004). The result shows how much a future amount of money is worth today. For example, if a person wanted to have $1,000,000 saved by the time they retire in 40 years, how much money do they have to invest in a lump sum today earning 10% interest? The present value = $1,000,000 divided by the interest compounded for 40 years. PV = $1,000,000/ (1.10)40 = $1,000,000/45.259 = $22,095. So $1 million 40 years from now at 10% interest has a present value of $22,095. Future value is the converse of present value in that it grows by the interest rate compounded each period for the number of years it is invested (Brealey, Myers, & Marcus, 2004). For example, a person gets a one-time gift from a rich aunt of $12,000 and invests that money in a 10-year CD at 8%. The value of that $12,000 in 10 years represents that money’s future value. FV = $12,000 x (1.08)10 = $12,000 x 2.159 = $25,907. The person has the opportunity to more than double his or her money by investing it rather than spending it today. This leads to the concept of doubling. People and investment advisors often talk about doubling their money. The rule of 72 says that the time it takes and investment to double is approximately equal to 72 divided by the interest rate expressed as a percentage (Brealey, Myers, & Marcus, 2004). For example, take the above example where a person received $12,000 from a rich aunt. How long would it take for that investment of $12,000 at 8% to double? It would take approximately 72/8 or 9 years to double in value. This formula works best with relatively low rates of interest and gives a close approximation of the length of time it take for money to double in value at a fixed interest rate (Brealey, Myers, & Marcus, 2004).

An annuity is an evenly spaced number of payments or money received in the same amount (Cedar Spring Software, Inc., 2002). Each TVM problem has five variables: interest rate or return, time or number of periods, future value, present value, and amount of payments either made or received (Brealey, Myers, & Marcus, 2004). The present value of annuity payments received over a number of years is less than if one had the full amount in hand now to invest. The reason for this is opportunity cost. If the full amount of the annuity could be invested today in a lump sum, the final value during the same term of the annuity would be much higher due to compound interest. So opportunity cost in this case is the total amount of the annuity payments over the length of the annuity and the value of investing the annuity’s total value today at a specified rate of return. For example, person is receiving annuity payments of $500 per month for 20 years will receive 12 x 500 x 20 = $120,000 during the annuity period . If that same person had $120,000 in his or her hand to invest today at a modest 6% interest compounded annually, they would have $120,000 x (1.06)20 = $384,856 at the end of the 20 years. The 0pportunity cost of this annuity is $384,856 - $120,000 = $264,856. This annuity caused the person to miss the opportunity to make an extra $264,856 over the 20-year period.

Money is more valuable when it can be invested and earn interest than if that same amount were promised in the future. The time value of money is the basis of finance and investing. The concepts that affect the time value of money are important to understand whether it be a business manager or a household manager. These ideas and concepts are so important in today’s climate of disappearing pensions, uncontrolled government spending and the likelihood that social security will not be around in 30 years. Steps should be taken to ensure that the nation’s children are taught these concepts in high school and college, so that the next generation will be prepared to manage their own financial well being.

References:

Brealey, R. A., Myers, S. C., & Marcus, A. J. (2004). Fundamentals of corporate finance (4th ed.). [University of Phoenix Custom Edition e-text]. New York, New York; McGraw Hill/ Irwin. Retrieved September 11, 2006, from University of Phoenix, Resource, FIN325 - Financial Analysis for Managers II website.

Cedar Spring Software Inc. (2002). Present value of an annuity. Retrieved September 14, 2006 from http://www.getobjects.com/Components/Finance/TVM/pva.html

Garrison, S. (2006). Time value of money. Retrieved September 14, 2006 from http://www.studyfinance.com/lessons/timevalue/index.mv

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