# Definition of Time Value of Money

### Concept of Time Value of Money

An important principle of finance is that the value of money is sensitive to the passage of time. Its amount and earning capacity in the present time is worth more than the same amount in the future.

The time value of money is a concept that the value of money is sensitive to the passage of time, whereby the purchasing power of money can increase or decrease by the mere passage of time. Future value is what an investment made today will be worth in the future. Present value is the value of current dollars of a future payment discounted to the present. An example of time value of money is if an investor invests one dollar today at a 5 percent annual interest rate, it increases to $1.05 in a year's time. This increase in money shows the value of that dollar over time. Conversely, in general, things become more expensive over time because of inflation. Inflation is the continual increase in the average price levels of goods and services. For instance, a snack item purchased today for one dollar may cost$1.05 in a year's time. This is because over time the production and other costs required to make that snack will likely increase, so the price of the snack will rise over time as well. Therefore, the dollar that could be used to buy that snack today will not be enough to purchase the same item in a year.

The only way to be able to afford the same snack a year from now is if the dollar today is invested to earn interest over time. If invested at 5 percent annual interest, it will increase to $1.05 in a year's time, the amount that's necessary to buy an identical snack item. Thus, one dollar in hand today is worth more than a dollar in hand a year from now. The real value of money is what can be bought with it today, but over time that value changes. Money that is being invested may be growing in value, while money that is being held but not spent or invested is declining in real value because of inflation. Consumers and businesses must consider the time value of money in determining whether or not to take out a loan as well as when and how to invest money. The interest rate is a crucial consideration when taking out a loan. A difference of a small amount of interest, such as 0.25 percent, can be worth tens of thousand or hundreds of thousands of dollars when a consumer takes out a 30-year mortgage loan. Expected returns on investments can be the difference between being able to retire early versus never being able to retire. When it comes to having money, more is better than less, and sooner is better than later. #### Time versus Dollar Graph ### How the Time Value of Money Affects Investments and the Economy Time value of money is the driving force behind investing and economic trading. An investment is an asset purchased with the goal of achieving financial gain. Some investments and marketable assets, including bonds, notes, stocks, and securities, are safer than others. Because of the importance of the time value of money when making investments, consumers and businesses must weigh the expected return of their investment against the risk of the investment and the amount of time it will take to produce that return. If an investor spends money today to buy a stock in a company, that investor is betting that over time the stock return from dividends, the portion of a company's earnings paid to shareholders, and appreciation, the increase in value over time, will outweigh other investment options. People also make personal investment risks based on similar calculus. When an individual commits to buying a house with a 30-year mortgage or sends their child to college with an expectation of paying the tuition for the next four years, they do so with the presumption that their job or current income source is secure for the amount of time they will need it to support those investments and that it will provide sufficient income to pay the mortgage and/or tuition bills. Businesses do the same when making investment choices. When a business decides to invest its earnings into building more factories or hiring more employees, it is essentially betting that the money spent today will produce a greater return in the future. A business could, instead, simply place its earnings in a bank or purchase government bonds that pay out low amounts of interest but are very safe. The business could also choose to risk its money by investing back in the business with the hope that the profits in the future will exceed the return it could realize from safer investments. In this case, when making its investment decision, the bank is balancing risk and possible return. This is the reason time value of money considerations are the most important when making investment choices and trading in the economic marketplace. Because of inflation, over time, the value of a dollar declines because costs always increase. Therefore, businesses and individuals alike must invest their money to generate a positive return, or their actual purchasing power will decline with any money that is being held and not invested. It is the ability to generate potential positive returns that encourages people to invest in stocks and bonds and to assume the risks of loans and other debt. ### Time Value of Money and Interest Rates The time value of a dollar can change based upon several inputs, such as the annual percentage rate or compound interest. An interest rate is the amount due per period, as a percentage of the amount owed at the end of the previous period. This rate is usually expressed in annual terms and noted as the annual percentage rate. The annual percentage rate (APR) is a measure that reflects the cost of borrowing money; it is determined as the interest rate charged each period multiplied by the number of periods in the year. This measure does not incorporate compounding. Compounding is the process of reinvesting an asset's earnings over an investment period to generate additional earnings above those generated by noncompounding earnings. Compound interest is the interest rate multiplied by the sum of any remaining unpaid principal and unpaid cumulative interest, as of the previous period. For an investor, compounding measures how an initial investment will grow over time as a certain amount of compound interest is added to the initial principal after a period of time. Then, as long as the money continues to be invested, additional compound interest is added to the initial investment. For example, assume Mary Nelson purchases a certificate of deposit (CD), a type of negotiable instrument usually issued by a bank or other financial institution that promises to pay a sum at a future date based on a given interest rate. If Mary's CD pays 20 percent APR compounded biannually, her investment of$1,000 will be worth 1,100 after six months, because 10 percent will be added to the initial principal. If Mary continues to leave the money invested in the CD for another six months, another 10 percent in interest will be added to both the original principal and the 10 percent of interest growth from the first six-month installment. There is a formula for calculating future value (FV). $\text{FV}=\text{PV}\;(1+r)^n$ Where: \begin{aligned}\text{FV}&=\text{Future Value}\\\text{PV}&=\text{Present Value}\\r&=\text{Interest Rate}\\n&=\text{Time Period}\end{aligned} After six months: \begin{aligned}\text{FV}&=\1{,}000\;(1+0.1)^1\\\\&=\1{,}100\end{aligned} After 12 months: \begin{aligned}\text{FV}&=\1{,}000\;(1+0.1)^2\\\\&=\1{,}210\end{aligned} This means that Mary would start out with1,000, have $1,100 after six months, and have$1,210 after one year, where, r is the interest rate and n is the number of times interest is compounded in a year.

In making investment decisions, investors need to know not only what interest rate their investment will generate but also the compounding rate. Regardless of the compounding rate, investors will seek to find out the APR, as it provides an equal comparison of different investment choices that may have different rates of return and different compounding schedules. Investors can account for inflation further when making investment choices. If an investor can estimate the inflation rate over a given period of time, they can make sure only to seek out investment opportunities meeting or, preferably, exceeding the rate of inflation. This helps to ensure purchasing power is not lost over time because of ineffective or nonexistent investments of the capital.

However, forecasting the rate of future inflation is a challenge beyond most investors' abilities. Even central banks, such as the U.S. Federal Reserve (Fed), have been challenged in accurately predicting future inflation rates. Therefore, investors look at the historical return rates of different investment assets, such as stocks and bonds, in selecting a portfolio of assets that are expected, based on historical data, to "beat" the rate of future inflation.

Investing early can often outweigh investing regularly. For example, for an investment with a return rate of 12 percent, investing at the beginning of the year $2,400 annually from age 19 to age 26 which is 7 investment periods and then no longer investing and letting the existing investment grow results in a total of$2,523,474 by age 65. Investing $2,400 annually from age 27 to age 65 results in a total of$1,838,619 by age 65. The early investor will earn $\2{,}523{,}474-\1{,}838{,}619=\684{,}855$ more than a late investor who invested $2,400 annually from age 27 until age 65. ### Investing Early Age Early Investor Return as of Year-End Late Investor Return as of Year-End 19$2,688 $0 25 27,119 0 27 34,018 2,688 30 47,793 12,847 35 84,228 39,717 40 148,439 87,071 45 261,600 170,526 50 461,029 317,601 55 812,491 576,798 60 1,431,887 1,033,592 65$2,523,474 \$1,838,619

Investing early can earn more overall than investing regularly at a later age.