## Calculating Future and Present Values

This calculator can be used to perform two time value of money, or TVM, calculations: future value and present values. The calculator needs a total of seven inputs, including:

- If a future value or present value calculation should be performed
- The total number of periods over which the calculation occurs
- The payment in each period. A negative value indicates the flow of money into the “investment” while a positive number indicates the flow is away from the investment. Typically, payments are modeled as negative values
- The interest rate, or discount rate
- Payment frequency, which can be annual, semiannual, quarterly, monthly, or weekly
- Whether payment occurs in the beginning of each period or at the end
- If you are calculating the future value, then enter any present value of the investment. If you are calculating present value, enter any future value of the investment

The calculator then provides the user with one output:

- Either the present value or the future value of the investment

### What is the Time Value of Money?

In finance, the time value of money, or TVM, is a core concept that a given sum of money today is worth more than it would be in the future. This is believed to be true for two reasons:

*The money can be invested and grow over time. For example, if 100 today can be invested at 10% per year, it will be worth 110 after one year. For this reason, 100 today is worth more than 100 a year from now – demonstrating the time value of money.**During inflationary times, 100 today can buy more than 100 a year from now. If prices are going up by 10% per year, then 100 a year from now will be able to buy 10% less than it could today.*

### Modeling the Time Value of Money

Is there really such a thing as a time value of money calculator? It’s certainly possible to calculate present value and future value. Both calculations demonstrate the time value of money, but there really isn’t such a thing as a time value of money calculator. If we ignore that technicality, we can dig deeper into the two concepts that demonstrate this finance concept – present and future value.

Earlier we said that a sum of money today is worth more than that same sum of money in the future. That 100 today is worth more than 100 next year. If we must wait one year for the 100, then we’ve lost the opportunity to grow that 100 by investing it. A present value calculation tells us how much that 100 in the future is worth today. It does this by discounting the value of 100. If our discount rate is 10%, then 100 received one year from now has a present value of 90.91 (100 / (1+10%)). In the same way, 100 received two years from now at a discount rate of 10% has a present value of around 82.64 (100 / (1+10%)^{2}). When we have a stream of cash flows into the future and we want to figure out how much that stream of cash flows is worth today, we would perform a present value calculation.

If we want to understand how fast an investment grows over time, we will calculate its future value. For example, if we were to invest 100 today at 10%, we would have 110 a year from now. That investment’s future value would be 110. Performing a future value calculation is much more common than present value calculations. For example, let’s say we set 100 a week aside for the next thirty years and we invest that money at 8%, roughly what the stock market has historically provided investors. In this example, set the calculator to Future Value, then model 52 (weeks) x 30 years or 1,560 periods at 8%. Our calculator tells us we would have 651,186.54 in our retirement account after 30 years.

### A Note on Payment Timing

When performing present or future value calculations, it’s important to indicate whether the payment occurs at the beginning or end of each period. This is especially true if the payments are annual. A payment made at the beginning of an annual cycle will have the interest rate assigned for one year, while an annual payment occurring at the end of a period will have no interest assigned in that year. Our calculator can demonstrate this point. Choose Future Value, Number of Periods (1), Payment per Period (-100), and Payment Frequency (Annual). Then switch the Payment Timing between Beginning and End and see how it affects the Future Value. It should fluctuate between 110 (if the payment is made at the beginning of the period) and 100 (if payment is made at the end of the period).