Present Value Calculator: Find PV of a Future Lump Sum
Calculate the present value of a future lump sum of money based on interest rate, number of periods and compounding frequency.
Calculate Present Value
| Result | Value |
|---|
All inputs must use the same time unit, for example years with an annual interest rate.
How the present value calculator works
The present value calculator works by discounting a future lump sum back to today using a fixed interest rate per compounding period. You enter the future value, the number of periods, the interest rate, and how often interest compounds, and the calculator returns the equivalent value of that money today.
Required inputs
Required inputs are the future value you expect to receive, the number of periods until you receive it, the annual nominal interest rate, and the compounding frequency per period. Choosing continuous compounding switches the calculation to the exponential discount formula automatically.
Present value formula explained
The present value formula divides the future value by one plus the periodic interest rate, raised to the power of the total number of compounding periods. Written as PV equals FV divided by the quantity 1 plus i raised to n, where i is the rate per compounding period and n is the total number of periods.
Worked example for present value
Worked examples make the formula concrete. If you want $10,000 in 2 years and your account earns 6.25 percent annually compounded monthly, the periodic rate i equals 0.0625 divided by 12, and n equals 12 times 2, or 24 periods. The result is a present value of approximately $8,827.83.
Present value interest factor explained
The present value interest factor, known as PVIF, is the discount multiplier applied to any future value under the same rate and period conditions. PVIF equals 1 divided by the quantity 1 plus i raised to n, so once calculated it can be reused by simply multiplying it by any future value.
Continuous compounding formula
Continuous compounding formula applies when compounding frequency increases without bound. In this case present value equals future value divided by e raised to the power of r times t, where e is approximately 2.71828, r is the annual interest rate as a decimal, and t is the number of years.
Reference table of present value variables
| Variable | Meaning |
|---|---|
| FV | Future value of the lump sum |
| t | Number of periods, commonly years |
| R, r | Annual nominal interest rate, r = R / 100 |
| m | Compounding frequency per period |
| i | Rate per compounding period, i = r / m |
| n | Total number of compounding periods, n = m × t |
| PV | Present value of the future sum |
| PVIF | Present value interest factor, 1 / (1 + i)^n |
Frequently asked questions
Present value is the current worth of a future sum of money, discounted back at a given interest rate. It answers the question of how much money you would need today to grow into a specific future amount under stated interest and compounding conditions.
The formula for present value of a future sum is PV equals FV divided by the quantity 1 plus i raised to the power n, where FV is the future value, i is the interest rate per compounding period, and n is the total number of compounding periods.
The present value interest factor, or PVIF, is the discount multiplier applied to a future value to find its present value. It equals 1 divided by the quantity 1 plus i raised to the power n, and can be reused for any future value under the same rate and period conditions.
Compounding frequency affects present value by changing the rate per period and the total number of periods used in the discount calculation. More frequent compounding, such as monthly instead of annually, results in a lower present value for the same nominal annual rate.
Continuous compounding occurs when the compounding frequency increases without limit. The present value formula becomes PV equals FV divided by e raised to the power r times t, where e is the mathematical constant approximately 2.71828, r is the annual rate and t is the number of years.
Present value is lower than future value because money available today can earn interest over time. Discounting a future amount back to today removes the interest it would have earned, so the present value is always less than the future value whenever the interest rate is positive.