### What is Future Value (FV)?

Future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth.

If, based on a guaranteed growth rate, a $10,000 investment made today will be worth$100,000 in 20 years, then the FV of the $10,000 investment is$100,000. The FV equation assumes a constant rate of growth and a single upfront payment left untouched for the duration of the investment.

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### Breaking Down Future Value

The FV calculation allows investors to predict, with varying degrees of accuracy, the amount of profit that can be generated by different investments. The amount of growth generated by holding a given amount in cash will likely be different than if that same amount were invested in stocks, so the FV equation is used to compare multiple options.

Determining the FV of an asset can become complicated, depending on the type of asset. In addition, the FV calculation is based on the assumption of a stable growth rate. If money is placed in a savings account with a guaranteed interest rate, then the FV is easy to determine accurately. However, investments in the stock market or other securities with a more volatile rate of return can present greater difficulty.

For the purposes of understanding the core concept, however, simple and compound interest rates are the most straightforward examples of the FV calculation.

### Future Value Using Simple Annual Interest

The FV calculation can be done one of two ways depending on the type of interest being earned. If an investment earns simple interest, then the formula is as follows, where I is the initial investment amount, R is the interest rate and T is the number of years the investment will be held:

﻿\begin{aligned} &FV=I\times\left(1+\left(R \times T\right)\right)\\ &\textbf{where:}\\ &I = \text{Investment Amount}\\ &R = \text{Interest Rate}\\ &T = \text{Number of years}\\ \end{aligned}﻿

For example, assume a $1,000 investment is held for five years in a savings account with 10% simple interest paid annually. In this case, the FV of the$1,000 initial investment is $1,000 * [1 + (0.10 * 5)], or$1,500.

### Future Value Using Compounded Annual Interest

With simple interest, it is assumed that the interest rate is earned only on the initial investment. With compounded interest, the rate is applied to each period's cumulative account balance. In the example above, the first year of investment earns 10% * $1,000, or$100, in interest. The following year, however, the account total is $1,100 rather than$1,000, so to calculate compounded interest, the 10% interest rate is applied to the full balance for second-year interest earnings of 10% * $1,100, or$110.

The formula for the FV of an investment earning compounding interest is:

﻿﻿\begin{aligned} &FV=I\times\left(1+R\right)^T\\ &\textbf{where:}\\ &I = \text{Investment Amount}\\ &R = \text{Interest Rate}\\ &T = \text{Number of years}\\ \end{aligned}﻿﻿

Using the above example, the same $1,000 invested for five years in a savings account with a 10% compounding interest rate would have a FV of$1,000 * [(1 + 0.10)5], or \$1,610.51.