How to Calculate the Future Value of an Investment
The ability to calculate the future value of an investment is a worthwhile skill. It allows you to make educated decisions about an investment or purchase regarding the return you may receive in the future.
When making a business case to invest money into a new project such as an acquisition, or an equipment purchase with a long holding period, it's important to have a way to calculate the potential return or profit you'll gain.
You can use any of three different ways to work the formula and get your answer. Each method uses a different means of calculation, but the underlying formula is the same in all three instances.
The Future Value Formula
A business case might be complex, but the formula's use can be demonstrated with a very simple example. If you have $100 to invest, and you can get an interest rate of 5 percent paid annually, what will the value of your investment be at the end of the first year?
The formula for the future value can be calculated with:
FVi = (PV + INT)
Where FV is future value, and i is the number of periods you want to calculate for. PV is the present value and INT is the interest rate.
You can read the formula, "the future value (FVi) at the end of one year equals the present value ($100) plus the value of the interest at the specified interest rate (5% of $100, or $5)."
FV1 = ( $100 + $5 ), or $105
The next formula presents this in a form that is easier to calculate. You could read (PV(1 + I)ⁿ) as, "the present value (PV) times (1 + I)ⁿ", where l represents the interest rate and the superscript ⁿ is the number of compounding periods.
FV = PV ( 1 + I )ⁿ
Using the example from above, in one year, your $100 lump sum investment earning 5 percent interest per year will equal:
FV = $100 ( 1 + 0.05 )1 = $105
In this instance, n is presented for reference. It does not need to be included if the value is one. To determine the value of your investment at the end of two years, you would change your calculation to include an exponent representing the two periods:
FV = $100 ( 1 + 0.05 )² = $110.25
This is how compounding interest is calculated. The long-form method, if your calculator can't handle exponents, is accomplished by calculating the value at the end of the first year, then multiplying the outcome by the same 5 percent rate for the second year:
FV = [ $100 ( 1 + 0.05 ) ] + [ $105 ( 1 + 0.05 ) ] = $110.25
You can continue this process to find the future value of the investment for any number of compounding periods.
FV = [ $100 ( 1 + 0.05 ) ] + [ $105 ( 1 + 0.05 ) ] + [$110.25 ( 1 + 0.05 ) ].....
Where the continuing periods mean you continue the calculation for the number of payment periods you need to determine.
Solving for a future value 20 years in the future means repeating the math 20 times. There are faster ways of calculating future value. Financial calculators and spreadsheets are designed to handle financial formulas.
Future Value Using a Financial Calculator
The formula for finding the future value of an investment on a financial calculator is:
FVN = PV ( 1 + I ) ⁿ
Although it doesn't quite look like it, this is the same formula used when you did the calculations manually.
Incidentally, you can use this formula with any calculator that has an exponential function key. However, using a financial calculator is better because it has dedicated keys corresponding to each of the four variables you'll be using, speeding up the process and minimizing the possibility of error. Here are the keys you will press:
- Press N and 2 (for 2 years' holding period)
- Press I/YR and 5 (for the interest rate of 5 percent)
- Press PV and -105 (for the amount of money we are calculating interest on in year 2)
Take note that you need to set the investment's present value as a negative number so that you can correctly calculate positive future cash flows. If you forget to add the "minus" sign, your future value will show as a negative number.
Press PMT and PMT (there are no payments beyond the first one)
Press FV, which returns the answer of $110.25
Future Value Using a Spreadsheet
Spreadsheets, such as Microsoft Excel, are well-suited for calculating time-value of money problems. The function that we use for the future value of an investment or a lump sum on an Excel spreadsheet is:
Where "rate" is the interest rate, "nper" is the number of periods, "pmt" is the amount of the payment made (if any, and it must be the same throughout the life of the investment), "pv" is present value, and "type" is when the payment is due. The payments due value is either a one (beginning of the month), or zero (end of the month).
To use the function in the worksheet, click on the cell you wish to enter the formula in. Enter the formula below and press enter.
You should receive a value of $105.
If you want to determine the future value at the end of two years (or any number of years), fill out the boxes as follows:
The result should be $110.25.