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Future Value of a Single Amount(Cheat Sheet)

Author:
Harold Averkamp, CPA, MBA

Future Value of a Single Amount

The future value of a single amount is also known as the future value of 1. The amount is a single, one-time deposit made at time period 0, which is also the beginning of period 1. It is assumed that the interest earned is added at the end of each time period.

Compounding of Interest

In the future value of a single amount, it is assumed that the interest added at the end of a time period will earn interest in the next time period. When the amount of interest earns interest, it is known as the compounding of interest. A single deposit that remains invested for many years at a high rate of interest will result in a very large amount.

Example 1. Assume that someone inherits $100,000 and the amount is deposited in an investment that is not taxed until the money is withdrawn. Also assume the money is never withdrawn and the investment earns a consistent 10% per year compounded annually. The following table illustrates how the single deposit of $100,000 will grow as a result of the compounding at 10% per year. (The amounts are approximate due to rounding.)

Rule of 72

The rule of 72 is a quick way to approximate either:

  • the number of years needed for an amount to double, or
  • the interest rate needed in order for an amount to double

Example 2. To illustrate how to approximate the number of years needed for an amount to double using the rule of 72, assume that an amount (or deposit) will earn 10% per year with the interest compounded at the end of each year. To determine the approximate number of years needed for the amount to double, divide 72 by the interest rate to be earned. Since 72 divided by 10 (the annual interest rate) = 7.2 years, a single amount compounded annually at 10% will double in 7.2 years.

In the table from Example 1, you will see that at the end of 7 years the future value is $194,872. This is nearly double the initial deposit of $100,000. At 7.2 years, the amount will be extremely close to $200,000 or double the $100,000 deposit.

Example 3. To illustrate how to approximate the interest rate needed for an amount to double in 7 years, divide 72 by 7 years. The result is a required interest rate of 10.3%.

Future Value of 1 Tables

In a classroom setting, future value of 1 (FV of 1) table which displays the future value factors is often used for instruction purposes. For instance, if you looked at an FV of 1 table, under the column with the heading of 10% and selected the row where the number of periods is 7, you would see the factor “1.94872”. This tells you that if $1 is invested at 10% and the interest is compounded annually for 7 annual periods, the $1 will grow to $1.95. Therefore, if you invest $100,000 at 10% interest for 7 years, it will grow to a future value of $194,872 ($100,000 X 1.94872). Note that this is the same as the amount we have in the table above.

Frequency of Compounded Interest

If the compounding of interest is done quarterly (instead of annually) for 7 years, the annual rate of 10% would be restated to be 2.5% per quarterly period; and the 7 annual periods will be restated to be 28 quarterly periods. The more frequent the compounding, the greater will be the future value.

Calculators

Instead of using a future value table or the rule of 72, it will be more precise and faster to use an online financial calculator. Electronic handheld financial calculators are also available.

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About the Author

Harold Averkamp

For the past 52 years, Harold Averkamp (CPA, MBA) has worked as an accounting supervisor, manager, consultant, university instructor, and innovator in teaching accounting online. He is the sole author of all the materials on AccountingCoach.com.

Learn More About Harold

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