- What is the definition of the future value (FV)?
- What formula calculates the future value (FV)?
- How is the future value (FV) and present value (PV) connected?
- What Excel function calculates the future value (FV)?
Future Value (FV) Definition
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 (FV) is calculated to estimate the value of an investment on a later date to guide decision-making.
The calculated future value (FV) 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:
- Simple Interest: The amount of interest earned is calculated off the original principal (or deposit) amount, which remains constant throughout the investment horizon.
- 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 (FV) Formula
The formula used to calculate the future value (FV) 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 (FV) 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 at an interest rate of 10% – assuming a compounding frequency of 1 – the investment should be worth $110 by the end of one year.
- Future Value (FV) = $100 × (1 + 10%) ^ 1
- FV = $110
However, if the interest compounds semi-annually, the investment is worth $121 instead.
- Future Value (FV) = $100 × (1 + 10%) ^ 2
- FV = $121
Future Value (FV) Excel Calculator
We’ll now move to a modeling exercise, which you can access by filling out the form below.
Future Value (FV) Calculation Example
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 (FV) 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
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.
If we enter our assumptions into the formula above, we get the following:
- Future Value (FV) = FV (0.5%, 24, 0, –$400,000)
- FV = $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
This tutorial demonstrates how to use the Excel FV Function in Excel to calculate the future value of an investment.
FV Function Overview
The FV Function Calculates the future value.
To use the FV Excel Worksheet Function, select a cell and type:
(Notice how the formula inputs appear)
FV Function Syntax and Inputs:
=FV(rate,nper,pmt,[pv],[type])rate – It’s the interest rate for each period.
nper – It’s the total number of payment periods.
pmt – It’s the payment per period.
pv – OPTIONAL: It’s the present value of the investment or the amount that the future payments are worth now. If the PV argument is omitted, it’s assumed to be zero (0). The pmt argument must be provided in case PV is omitted.
type – OPTIONAL: The value of this argument is either 0 or 1, which shows if the payment is due at the end of the period, 0 and the beginning of the period, 1. If the type argument is omitted then its default value is considered 0 i.e. the payment is due at the end of the period.
It’s the value of the investment at a particular date in the future that is equivalent in value to a specified sum today.
The Future Value is calculated in two ways:
- Future Value Using Simple Annual Interest Rate is calculated as:
- Future Value Using Compounded Annual interest Rate is calculated as:
Where:
I = Invested Amount
R = Interest Rate
T = Number of periods
What Is Excel FV Function?
FV is used to determine how much the investment will be worth at the end of the given period if there are regular and constant deposits at constant interest rates.
Calculate Future Value of Savings
Suppose, we deposited $1,000 for 4 years into a savings account. The interest we get from this was 8% annually, which was compounded monthly and with no additional payments.
The annual interest rate is converted into monthly interest as
Monthly Interest Rate – 8% (annual interest rate) / 12 (months per year) = 0.67%
and the number of payments per period is converted into the monthly number of payments as
NPER – 5 (years) * 12 (months per year) = 60
No regular payments are being made, so the value of pmt argument is
PMT = 0
The formula used for the calculation is:
=FV(D7,D8,D9,D10,D11)The Future Value of the investment is
FV = $1,492.81
Calculate Future Value of an Investment
Let’s take a look at another example, where $10,000 has been invested at 10% compounded monthly for 4 years. And on top of the initial deposit, an additional amount of $500 are planned to be invested each month for the next four years. So the future value of the total savings would be calculated with the help of excel FV Formula.
As the payments are made monthly, the annual interest rate is converted into monthly interest by
Monthly Interest Rate – 10% (annual interest rate) / 12 (months per year) = 0.83%
and the number of payments per period is converted into the monthly number of payments by
NPER – 4 (years) * 12 (months per year) = 48
The formula used for the calculation is:
=FV(D7,D8,D9,D10,D11)So, the accumulated amount at the end of the 4th year would be
FV = $44,206.83
All of the above examples work exactly the same in Google Sheets as in Excel.
Additional Notes
Use the FV Function to calculate the Future Value of an investment.
Investopedia defines future value as: The value of an asset or cash at a specified date in the future that is equivalent to a specified sum today.
Make sure the units of nper and rate are consistent, i.e. in case of monthly interest rate the number of periods of investment should also be in months.
In the Financial Functions the cash outflows, such as deposits, are represented by negative numbers and the cash inflows, such as dividends, are represented by positive numbers.
FV Examples in VBA
You can also use the FV function in VBA. Type:
application.worksheetfunction.fv(rate,nper,pmt,pv,type)
For the function arguments (rate, etc.), you can either enter them directly into the function or define variables to use instead.
Return to the List of all Functions in Excel