   # Future Value (FV)

Guide to Understanding Future Value (FV) ## How to Calculate Future Value (Step-by-Step)

The future value (FV) is a fundamental concept to corporate finance, whether it be for determining the valuation of a potential investment or projecting cash flows to support capital budgeting decisions.

For investors and corporations alike, the future value is calculated to estimate the value of an investment on a later date to guide decision-making.

The calculated future value is a function of the interest rate assumption – i.e. the rate of return earned on the original amount of capital invested, or the present value (PV).

The present value (PV) is defined as the initial investment amount, whereas the future value represents the ending amount, with the original amount as well as any accumulated interest.

The “time value of money” states that a dollar today is worth more than a dollar tomorrow, so future cash flows must be discounted back to the present date to be comparable to present values.

There are two types of interest:

1. Simple Interest: The amount of interest earned is calculated off the original principal (or deposit) amount, which remains constant throughout the investment horizon.
2. Compound Interest: The incremental amount of interest earned is calculated off the original principal amount (or deposit) and the accrued interest to date, i.e. “interest on interest”.

## Future Value Formula (FV)

The formula used to calculate the future value is shown below.

Future Value (FV) = PV × (1 + r) ^ n

Where:

• PV = Present Value
• r = Interest Rate (%)
• n = Number of Compounding Periods

The number of compounding periods is equal to the term length in years multiplied by the compounding frequency.

The more compounding periods there are, the greater the future value is going to be.

• Annual Compounding = 1x
• Semi-Annual Compounding = 2x
• Quarterly Compounding = 4x
• Monthly Compounding = 12x
• Daily Compounding = 365x

For example, if you decided to invest \$100.00 at an interest rate of 10% – assuming a compounding frequency of 1 – the investment should be worth \$110 by the end of one year.

• FV = \$100 × (1 + 10%) ^ 1 = \$110.00

However, if the interest compounds semi-annually, the investment is worth \$121 instead.

• FV = \$100 × (1 + 10/2%) ^ 2 = \$110.25

## Future Value Calculator (FV) – Excel Model Template

We’ll now move to a modeling exercise, which you can access by filling out the form below. Submitting ...

## Step 1. FV Calculation Exercise Assumptions

Suppose you deposited \$400,000 into a bank account with an annual interest rate of 0.5%, which compounds quarterly.

If we assume that the term length is 6 years – the following are the inputs to calculate the future value of the deposit.

• Present Value (PV) = \$400,000
• Interest Rate (r) = 0.5%
• Term Length (t) = 6 Years
• Compounding Frequency = Quarterly (4x)

Since the number of compounding periods is equal to the term length (6 years) multiplied by the compounding frequency (4x), the number of compounding periods is 24.

• Number of Compounding Periods (nper) = 24

## Step 2. Calculate Future Value in Excel (“FV” Function)

The “FV” Excel function can be used to calculate how much the original \$400,000 deposit is worth after a six-year time frame.

“= FV (rate, nper, pmt, pv)”

On the date of the deposit, the \$400,000 was an outflow (i.e. an investment) from your perspective, so the amount should be entered with a negative sign in front.

## Step 3. Future Value Calculation Analysis (Compounding Frequency)

If we enter our assumptions into the formula above, we get the following:

• FV (0.5%, 24, 0, –\$400,000) = \$450,864

So your \$400,000 deposit has grown to \$450,864 after six years of remaining in the account, which paid an interest rate of 0.5% compounded on a quarterly basis.

The more frequently that the deposit is compounded, the greater the amount of interest earned, which we can confirm by adjusting the compounding frequency.

• Annual Compounding = \$412,151
• Semi-Annual Compounding = \$424,671
• Quarterly Compounding = \$450,864
• Monthly Compounding = \$572,818  Step-by-Step Online Course

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