Time Value of Money

What is Time Value of Money?

    The time value of money is a fundamental financial principle stating that money obtained in the present is more valuable than the same amount of money acquired in the future. This is true because the money you have now can be invested and produce a return, therefore increasing your wealth in the future.

Why is that though? Time value of money is tied to inflation and purchasing power. In addition to the rate of return that may be obtained by investing the money. All aspects must be considered. During these times, inflation is especially significant when it constantly erodes the value of the present value of money.

Let’s pull out our Investment 101 textbook now and break down the formula. There are different methods to alter the formula for time value of money, but our focus will be on determining the future value.

FV = PV * [1 + (i/n)]^(n * t)

Where: 

  • FV = Future Value of Money
  • PV = Present Value of Money
  • i = Interest Rate Earned on the Money
  • t = The Period of Time the Money is Held
  • n = The Amount of Compounding Periods of Interest Per Year

Example time! Let’s say you currently want to invest $10,000 and expect a return of 6% compounded annually each year for the next 3 years. You can determine the future value of your $10,000 investment as follows:

FV = $10,000 * [1 + (6%/1)]^(1 * 3) = $11,910.16

Why is it Important?

    The concept of the time value of money is crucial not only for individuals but also for making business decisions. When making decisions about investing in new product development, acquiring new business equipment or facilities, and arranging credit conditions for the sale of their products, businesses consider the time value of money.

How therefore can one optimize the time value of money? The following table explains the significance of each component of time value of money with respect to Future Value.

Components

Explanation


Present Value

The principal amount is the foundation of a person's potential earnings and can be increased by making contributions to the investment. This is decided by the investor's financial state.


Interest Rate

The rate of return on the investment is significant since it determines the amount of interest added to the principal. However, here is where diversification plays a role and determined by the risk tolerance.


Time

The period of time that the investment can be held to grow is crucial (will be shown below on how important this is). The time is decided by the investor's time horizon and the needs for the funds.


Compounding Periods

The frequency of interest being compounded is significant because compound interest incorporates interest accrued in prior periods, it increases at an ever-increasing rate.

The Power of Time Value of Money

    Time to bring everything together by assessing each feature and how much growth can be achieved by modifying the variables. The first plot below shows the change in time if an investor started at year 0, year 10, and year 20. The second plot shows the rate of return if the investment earned 5%, 6%, or 7%. The last plot shows the difference in frequency for the investment annually, semiannually, and quarterly.

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    The first factor (Time) clearly demonstrates the advantage of investing as soon as possible. In this instructional scenario, the investor who began investing in year 0 would be better off by $827k compared to the person who began investing in year 1o. When you compare it to the investor that started in year 20, the investor would be better off by $1.25 million by starting at year 0.

Furthermore, if we turn our attention to the possible interest rates that investors could earn, we observe additional differences. The change in 100 bps (1%), we see a difference of $300k (5% to 6%) to $400k (6% to 7%). However, there is more that goes into earned interest rates like the ability to take risks & the preference for risk

Lastly is the change in the frequency of the investment. In this case, it looked at the difference in annual, semiannual, and quarter frequency. Even though the difference may seem small compared to the other plots, it plays a crucial role in interest rates. This is because interest on mortgages, credit cards, or even bonds are compounded differently. Clearly, the difference is negligible in the near term, but suppose your mortgage is compounded quarterly instead of annually. The difference is $133k and it will add up once the frequency is increased to monthly or even daily!

Overall, each aspect has its importance in time value of money, and knowing how each interacts with the other can help with many life decisions

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