Present Value Calculator
Enter a future amount, an annual discount rate, the number of years and an optional payment received at the end of each period. Choose whether to discount once a year or monthly. With Monthly, the payment comes every month and the rate is divided by 12. The calculator returns one figure, the value today of the amount and the payments, rounded to the cent.
How to use the Present Value Calculator
- Enter your numbers in the Present Value Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The present value formula
PV = FV / (1 + r)^n + PMT × [(1 − (1 + r)^−n) / r]
r is the annual rate as a decimal, n is the number of years and PMT is the payment at the end of each year. The first term discounts the single future amount, the second the payments. At a rate of 0 the present value is FV + PMT × n. Negative rates work too, as long as they stay above −100%. With Monthly, r is the annual rate divided by 12, n is the number of years times 12 and PMT is the payment at the end of each month.
Worked example
Receiving $50,000 in 10 years at a 5% annual rate: PV = 50,000 / 1.05^10 = $30,695.66. A payment of $5,000 at the end of each of those 10 years is worth 5,000 × (1 − 1.05^−10) / 0.05 = $38,608.67 today. Enter both and the calculator shows $69,304.34. That is a cent more than the two rounded figures added, because the calculator rounds only the total. With Monthly, the same $50,000 discounted at 5% / 12 for 120 months is worth $30,358.05 today, and $500 at the end of each of those months is worth 500 × (1 − (1 + 0.05/12)^−120) / (0.05/12) = $47,140.68. Enter both and the calculator shows $77,498.73.
Frequently asked questions
How often does the calculator discount?
Once a year or monthly, as you choose. The rate is always an annual rate and the term is always in years. Once a year, the payment arrives at the end of each year. With Monthly, it arrives at the end of each month. The calculator has no start-of-period option.
What does monthly do to the result?
The same future amount is worth less today, because 5% / 12 each month compounds to more than 5% a year: $50,000 in 10 years is $30,695.66 discounted once a year and $30,358.05 discounted monthly. Payments that arrive through the year are worth more than the same total paid at each year end: $500 a month comes to $47,140.68, and $6,000 at each year end to $46,330.41.
What if my rate is an effective annual rate?
Monthly divides the rate you enter by 12, as a loan or savings rate works. For an effective annual rate, turn it into the rate to enter first: 12 × ((1 + rate)^(1/12) − 1). An effective 5% is about 4.889%.
How do PV and NPV differ?
NPV (Net Present Value) sums the PV of all cash flows including the initial investment (a negative number). This calculator has no field for an initial investment, so it returns the PV of the amount and the payments only. The IRR calculator takes an initial investment and yearly cash flows and shows the NPV at a rate you choose.
Why does the same dollar shrink over time?
Because dollars today can be invested to grow. The discount factor 1/(1+r)^n captures the opportunity cost of receiving money later instead of now.