Future Value, Single Amount
buttons.Single-Period Investment
Since the number of periods (n or t) is one, FV=PV(1+i), where i is the interest rate.
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 are 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:
- Present Value (PV)
- Future Value (FV)
- Interest Rate (i or r) [Note: for all formulas, express interest
in its decimal form, not as a whole number. 7% is .07, 12% is .12, and
so on. ]
- Number of Periods (t or n)
In a single period, there is only one formula you need to know:
FV=PV(1+i). The full formulas, which we will be addressing later, are as
follows:
Compound interest: \(FV=PV⋅(1+i)^t\).
Simple interest: \(FV=PV⋅(1+rt)\)
We will address these later, but note that when \(t=1\), both formulas become \(FV=PV⋅(1+i)\).
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 FV=100(1+.03), so FV=100(1.03), so FV=103. Your balance will be $103 in one year.
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.
Terms
- Single-Period Investment – An investment that takes place over one period, usually one year.
- Multi-Period Investment – An investment that takes place over more than one periods.
- Periods (t or n) – Units of time. 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 FV=100(1+.05). FV=100(1.05) FV=$105.
Source: Boundless Finance, https://ftp.worldpossible.org/endless/eos-rachel/RACHEL/RACHEL/modules/en-boundless-static/www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/future-value-single-amount-55/index.html
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 License.