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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. A business case might be complex, but the formula's use can be demonstrated with a very simple example. 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. The next formula presents this in a form that is easier to calculate. 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:.

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:. You can continue this process to find the future value of the investment for any number of compounding periods.

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.

The formula for finding the future value of an investment on a financial calculator is:. 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. As the name suggests, this function is designed to solve for the number of periods and is defined as:.

NPer rate , pmt , pv , fv , type. You can see that it will take 8.

### The Future Value of a Dollar

One important thing to note is that you absolutely must enter your according to the cash flow sign convention. If you don't make either the PV or FV a negative number and the other one positive , then you will get a NUM error instead of the answer. That is because, if both numbers are positive, Excel thinks that you are getting a benefit without making any investment. If you get this error, just fix the problem by changing the sign of either PV or FV. In this problem it doesn't really matter which one is negative.

The key is that they must have opposite signs. You can prove this by changing the PV to 1 and the FV to 2. You will get exactly the same answer. Solving for the interest rate is quite common.

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## Future Value vs. Present Value

Maybe you have recently sold an investment and would like to know what your compound average annual rate of return was. Or, perhaps you are thinking of making an investment and you would like to know what rate of return you need to earn to reach a certain future value. Let's return to our college savings problem from above , but we'll change it slightly.

Finding the interest rate in a time value of money problem requires the use of the Rate function, which is defined as:. Rate nper , pmt , pv , fv , type , guess. Note that the Guess argument is rarely required and is optional.

### Find the best rates for...

In most cases, you can just leave it out. It is included for those times only when dealing with annuities when there are two or more solutions to the problem. Typically, this only happens when you are dealing with uneven cash flows and there are sign changes in the cash flow stream.

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Create a new worksheet and enter the data as shown above. As before, we need to be careful when entering the PV and FV into the function.

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Therefore, we entered , for PV, and , into FV. Again, if you get NUM instead of an answer, it is because you didn't follow the cash flow sign convention. Therefore, in order to reach the same goal, you would need to earn a higher interest rate. When you have solved a problem, always be sure to give the answer a second look and be sure that it seems likely to be correct.

This requires that you understand the calculations that the functions are doing and the relationships between the variables.