How To Use the Future Value Formula

What Is Future Value?

Future value (FV) is the value of a current asset at a future date based on an assumed growth rate. Investors and financial planners use it to estimate how much an investment today will be worth in the future.

External factors such as inflation can adversely affect an asset's future value. Future value can be contrasted with present value (PV).

Future Value Formula

The future value calculation allows investors to project the amount of profit that can be generated by assets. The future value of an asset depends on the type of investment because the future value formula assumes a stable growth rate.

If money is placed in a savings account with a guaranteed interest rate, then the future value is easy to determine accurately. However, investments in the stock market or in other securities with a volatile rate of return can yield different results.

Simple Annual Interest

The future value formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment. If an investment earns simple interest compounded annually, then the FV formula is:

$\begin{aligned}&FV=PV\times(1+r)^n\\&\textbf{where:}\\&FV=\text{Future value}\\&PV=\text{Present value}\\&r=\text{Interest rate per period}\\&n=\text{Number of periods}\end{aligned}$​FV=PV×(1+r)nwhere:FV=Future valuePV=Present valuer=Interest rate per periodn=Number of periods​

If a $1,000 investment is held for five years in a savings account with 10% simple interest paid annually, the FV of the $1,000 investment is:

FV = $1,000 × [1 + (0.10 x 5)]

FV = $1,500.

Compounded Annual Interest

With compound 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.

To compound 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:

$\begin{aligned}&FV=PV\times(1+r)^{nt}\\&\textbf{where:}\\&FV=\text{Future value}\\&PV=\text{Present value}\\&r=\text{Interest rate per period}\\&n=\text{Number of periods}\\&t=\text{Time in years}\end{aligned}$​FV=PV×(1+r)ntwhere:FV=Future valuePV=Present valuer=Interest rate per periodn=Number of periodst=Time in years​

Using the above example, the same $1,000 invested for five years in a savings account with a 10% compounding interest rate would have an FV of:

FV = $1,000 × [(1 + 0.10)⁵]

FV = $1,610.51

Benefits

• Future value allows for planning. Individuals can plan for the future as they understand their financial position. For example, a homebuyer attempting to save $100,000 for a down payment can calculate how long it will take to reach these savings by using future value.
• Future value makes comparisons easier. By calculating future values and comparing results, an investor can compare options. For instance, one option requires a $5,000 investment that will return 10% for the next 3 years. The other requires a $3,000 investment that will return 5% in year one. That's 10% in year 2, and 35% in year 3.
• Future value is easy to calculate due to estimates. Because it relies on estimates, anyone can use future value in hypothetical situations. For example, the homebuyer above trying to save $100,000 could calculate the future value of their savings using their estimated monthly savings, estimated interest rate, and estimated savings period.

Limitations

• Future value usually assumes constant growth. Growth may not always be linear or consistent year-over-year.
• Future value assumptions may be false. If the market fails to produce the estimated return, the calculated value will prove worthless.
• Future value may not work for comparisons. Future value returns a final dollar value for what something will be worth at some future date. Therefore, there are some limitations when comparing projects. Looking at only future value, one option may appear favorable because it has a higher value, but the decision-maker may fail to consider the starting point of the initial investment.

Future Value vs. Present Value

The concept of future value is often closely tied to the concept of present value. Future value calculations determine the value of something in the future and present value finds what something in the future is worth today. Both concepts rely on discount or growth rates, compounding periods, and initial investments.

Future Value: $1,000 * (1 + 5%)^1 = $1,050

The future value formula could be reversed to determine how much something in the future is worth today. In other words, assuming the same investment assumptions, $1,050 has the present value of $1,000 today.

Present Value: $1,050 / (1 + 5%)^1 = $1,000

By changing directions, future value can derive present value and vice versa. The future value of $1,000 one year from now invested at 5% is $1,050, and the present value of $1,050 one year from now, assuming 5% interest, is $1,000.

Examples

1. The Internal Revenue Service imposes a Failure to File Penalty on taxpayers who do not file their returns by the due date. The penalty is calculated as 5% of unpaid taxes for each month a tax return is late, up to a limit of 25% of unpaid taxes.

If a taxpayer knows they have filed their return late and are subject to the 5% penalty, that taxpayer can easily calculate the future value of their owed taxes based on the imposed growth rate of their fee.

The taxpayer expects to have a $500 tax obligation. The taxpayer can calculate the future value of their obligation assuming a 5% penalty imposed on the $500 tax obligation for one month. In other words, the $500 tax obligation has a future value of $525 when factoring in the liability growth due to the 5% penalty.

2. Consider a zero-coupon bond trading at a discount price of $950. The bond has two years to maturity with a target yield to maturity of 8%. If an investor is interested in knowing what the value of this bond will be in two years, they can calculate the future value based on the current variables.

In two years, the future value of this bond will be $1,108.08 ($950 * ((1 + 8%)^2).

Investors can utilize calculators available through Treasury Direct, the U.S. Department of Treasury bond website, to estimate the growth and future value of savings bonds.

The Bottom Line

Future value is a key concept in finance that draws from the time value of money concept. Using future value, investors can estimate what the value of an investment (or series of cash flows) today would be at some point later in time. Future value works inversely to present value, which involves discounting future cash flows to derive a present value.