Future Value, Single Amount

Single-Period Investment

What is the difference between simple and compounding interest? Read this section to learn how to calculate the future value of a single-period investment, calculate the future value of a multi-period investment with simple and complex interest rates, and distinguish between calculating future value with simple interest and with compound interest.

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.