As the interest rate increases for any given period, the future value interest factor will

What Is Future Value (FV)?

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

Knowing the future value enables investors to make sound investment decisions based on their anticipated needs. However, external economic factors, such as inflation, can adversely affect the future value of the asset by eroding its value.

Future value can be contrasted with present value (PV).

Key Takeaways

• Future value (FV) is the value of a current asset at some point in the future based on an assumed growth rate.
• Investors are able to reasonably assume an investment’s profit using the FV calculation.
• Determining the FV of a market investment can be challenging because of market volatility and uncertainty about future investment conditions.
• There are two ways of calculating the FV of an asset: FV using simple interest, and FV using compound interest.
• Future value is opposed by present value (PV); the former calculates what something will be worth at a future date, while the other calculates what something at a future date is worth today.

Future Value

Understanding Future Value (FV)

The future value 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; therefore, the future value equation is used to compare multiple options.

Determining the future value of an asset can become complicated, depending on the type of asset. Also, the future value 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 future value 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.

To understand the core concept, however, simple and compound interest rates are the most straightforward examples of the future value calculation.

Formula and Calculation of Future Value

Future Value Using 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. The future value calculation can be done one of two ways, depending on the type of interest being earned. If an investment earns simple interest, then the FV formula is:

F V = I × ( 1 + ( R × T ) ) where: I = Investment amount R = Interest rate T = Number of years \begin{aligned} &\mathit{FV} = \mathit{I} \times ( 1 + ( \mathit{R} \times \mathit{T} ) ) \\ &\textbf{where:}\\ &\mathit{I} = \text{Investment amount} \\ &\mathit{R} = \text{Interest rate} \\ &\mathit{T} = \text{Number of years} \\ \end{aligned} ​FV=I×(1+(R×T))where:I=Investment amountR=Interest rateT=Number of years​

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 x 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:

F V = I × ( 1 + R ) T where: I = Investment amount R = Interest rate T = Number of years \begin{aligned}&\mathit{FV} = \mathit{I} \times ( 1 + \mathit{R})^T \\&\textbf{where:}\\&\mathit{I} = \text{Investment amount} \\&\mathit{R} = \text{Interest rate} \\&\mathit{T} = \text{Number of years}\end{aligned} ​FV=I×(1+R)Twhere:I=Investment amountR=Interest rateT=Number of 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 $1,000 × [(1 + 0.10)5], or $1,610.51.

Bearish about the market? Future value can also handle negative interest rates to calculate scenarios such as how much $1,000 invested today will be worth if the market loses 5% each of the next two years.

Pros and Cons of Future Value

Future value can be useful in some situations. However, there are limitations to the calculation, and it may not be suitable for use in some cases.

Advantages of Future Value

• Future value allows for planning. A company or investor may know what they have today, and they may be able to input some assumptions about what will happen in the future. By combining this information, people 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 this savings by using future value.
• Future value makes comparisons easier. Let's say an investor is comparing two investment options. One 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, 10% in year 2, and 35% in year 3. The only way an investor will know which investment may make more money is by calculating the future values and comparing the results.
• Future value is easy to calculate due to estimates. Future value does not require sophisticated or real numbers. Because it is heavily reliant on estimates, anyone can use future value in hypothetical situations. For example, regarding the homebuyer above trying to save $100,000, that person can calculate the future value of their savings using their estimated monthly savings, estimated interest rate, and estimated savings period.

Disadvantages of Future Value

• Future value usually assumes constant growth. In the formulas above, only one interest rate is used. Although it is possible to calculate future value using different interest rates, calculations get more complex and less intuitive. In exchange for a simplified formula using only rate, a situation may have unrealistic parameters as growth may not always be linear or consistent year-over-year.
• Future value assumptions may not actually happen. Because future value is based on future assumptions, the calculations are simply estimates that may not truly happen. For example, an investor may have calculated the future value of their portfolio estimated the market would return 8% each year. When the market fails to produce that estimated return, the future value calculation from before is worthless.
• Future value may fail at comparisons. Future value simply returns a final dollar value for what something will be worth in the future. Therefore, there are some limitations when comparing two projects. Consider this example: an investor can choose to invest $10,000 for an expected 1% return or can choose to invest $100 for an expected 700% return. Looking at only future value, the first option would appear favorable because it is higher; it fails to consider the starting point of the initial investment.

Future Value Pros & Cons

Pros

• Relies on estimates, therefore it is easy to calculate.

• Future value calculations of lump sum or simple cashflows may be easy to calculate.

• Future value can singlehanded determine whether an investor meets a target or goal.

• The concept of future value can be applied to any cashflow, return, or investment structure.

Cons

• Relies on estimates, therefore findings may be quickly invalidated.

• Future value calculations of annuities or irregular cashflow may be difficult to calculate.

• Future value by itself cannot be used to compare and choose between two mutually exclusive projects.

• Most future value models assume constant rate growth which is often impractical.

Future Value vs. Present Value

The concept of future value is often closely tied to the concept of present value. Whereas future value calculations attempt to figure out the value of something in the future, present value attempts to figure out what something in the future will be worth today.

Both concepts rely on the same financial principles (i.e. discount or growth rates, compounding periods, initial investments, etc.). Each component is related and inherently feed into the calculation of the other. For example, imagine having $1,000 on hand today and expecting to earn 5% over the following year.

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

Therefore, 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 earned is $1,000.

Annuity vs. Annuity Due

When calculating future value of an annuity, understand the timing of when payments are made as this will impact your calculation. If payments are made at the end of a period, it is an ordinary annuity. If payments are made at the beginning of a period, it is an annuity due.

Example of Future Value

The Internal Revenue Service imposes a Failure to File Penalty on taxpayers who do not file their return 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. An additional Failure to Pay penalty can also be assessed, and the IRS imposes interest on penalties.

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.

For example, consider if a taxpayer anticipates filing their return one month late. 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.

Consider another example of a zero-coupon bond trading at a discount price of $950. The bond has two years left to maturity and has a target yield to maturity is 8%. If an investor is interested in knowing what the value of this bond will be in two years, they can simply 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). Through TreasuryDirect, the U.S. Department of Treasury bond website, investors can utilize calculators to estimate the growth and future value of savings bonds.

What Is Future Value?

Future value (FV) is a financial concept that assigns a value to an asset based on estimated variables such as future interest rates or cashflows. It may be useful for an investor to know how much their investment may be in five years given an expected rate of return. This concept of taking the investment value today, applying expected growth, and calculating what the investment will be in the future is future value.

How Do I Calculate Future Value?

There are several formulas to calculate future value. In all of them, the concept is the same: future value is calculated by taking cashflows and projecting them forward based on anticipated growth rates. Simple future value calculations regarding a single lump sum are easier to calculate (principal * (1 + rate) ^ periods), while future value calculations of annuities, varying cash flows, or varying interest rates are more complex.

What Is Future Value Used for?

Future value is used for planning purposes to see what an investment, cashflow, or expense may be in the future. Investors use future value to determine whether or not to embark on an investment given its future value. Future value can also be used to determine risk, see what a given expense will grow at if interest is charged, or be used as a savings target to understand whether enough money will be reserved given the current pace of savings and expected rate of return.

What Is the Future Value of an Annuity?

The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

FV of an annuity is calculated as:

FV = PMT x [(1+r)n - 1)]/r

​where:

• FV = Future value of an annuity stream
• PMT = Dollar amount of each annuity payment
• r = The discount (interest) rate
• n = Number of periods in which payments will be made

How Is Future Value Different From Present Value?

Future value takes a current situation and projects what it will be worth in the future. For example, future value would estimate the value of $1,000 today invested at 10% interest for 5 years. Alternatively, present value takes a future situation and projects what it is worth today. For example, present value would estimate how much money you would need to have today to invest at 10% for 5 years to end up with $1,000.

The Bottom Line

Future value (FV) is a key concept in finance that draws from the time value of money: a dollar today is worth relatively more than a dollar in the future. Using future value, once can estimate the value of that dollar at some point later in time, or the value of an investment or series of cash flows at that future date. In general, the future value of a sum of money today is calculated by multiplying the amount of cash by a function of the expected rate of return over the expected time period. Future value works in the opposite way as discounting future cash flows to the present value.

What happens to future value if interest rate increases?

What is the future value interest factor?

What happens to the future value of an annuity when the time period increases?

How is the present value interest factor related to the future value interest factor?