Future Value, Single Amount

Read this section that discusses four separate but related concepts. They include: (1) multi-period investment, (2) approaches to calculating future value, and (3) single-period investment. How are these topics used in the business world? Applying these concepts is helpful when comparing alternative investments and when scarce capital resources are available. Often in a business setting, limited capital resources are available. Therefore, deciding which investment is best depends on comparing which investments will bring the highest returns to the business.

Single-Period Investment

Since the number of periods (n or t) is one, F V=P V(1+i), where i is the interest rate.


  • Calculate the future value of a single-period investment


Key Points
  • Single-period investments use a specified way of calculating future and present value.
  • Single-period investments take place over one period (usually one year).
  • In a single-period investment, you only need to know two of the three variables PV, FV, and i. The number of periods is implied as one since it is a single-period.

Key Terms
  • Multi-period investment: An investment that takes place over more than one periods.
  • Periods (t or n): Units of time. Usually one year.
  • Single-period investment: An investment that takes place over one period, usually one year.


  • What is the value of a single-period, $100 investment at a 5% interest rate? PV=100 and i=5 \% (or  .05) so \mathrm{FV}=100(1+.05). \mathrm{FV}=100(1.05) \mathrm{FV}=$105.

The amount of time between the present and future is called the number of periods. A period is a general block of time. Usually, a period is one year. The number of periods can be represented as either t or n.

Suppose you're making an investment, such as depositing your money in a bank. If you plan on leaving the money there for one year, you're making a single-period investment. Any investment for more than one year is called a multi-period investment.

Let's go through an example of a single-period investment. As you know, if you know three of the following four values, you can solve for the fourth:

  1. Present Value (PV)
  2. Future Value (FV)
  3. Interest Rate (i or r) [Note: for all formulas, express interest in it's decimal form, not as a whole number. 7% is .07, 12% is .12, and so on. ]
  4. Number of Periods (t or n)

In a single-period, there is only one formula you need to know: F V=P V(1+i). The full formulas, which we will be addressing later, are as follows:

Compound interest: \mathrm{FV}=\mathrm{PV} \cdot(1+\mathrm{i})^{\mathrm{t}}.

Simple interest: \mathrm{FV}=\mathrm{PV} \cdot(1+\mathrm{rt}).

We will address these later, but note that when t=1 both formulas become \mathrm{FV}=\mathrm{PV} \cdot(1+\mathrm{i}).

For example, suppose you deposit $100 into a bank account that pays 3% interest. What is the balance in your account after one year?

In this case, your PV is $100 and your interest is 3%. You want to know the value of your investment in the future, so you're solving for FV. Since this is a single-period investment, t (or n) is 1. Plugging the numbers into the formula, you get F V=100(1+.03) so \mathrm{FV}=100(1.03) so F V=103. Your balance will be $103 in one year.

Source: Boundless
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