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.


LEARNING OBJECTIVE

  • Calculate the future value of a single-period investment


KEY TAKEAWAYS

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.


EXAMPLE

  • 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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