How to use the present value calculator
Use Future money to find what a single amount you will get later is worth today: enter the future value, the number of periods and the interest rate. Use Periodic deposits for a series of equal payments: enter the number of periods, the rate, the payment and whether it is made at the beginning or the end of each period. The second tab also shows the future value of the payments, a growth graph and a schedule you can export as CSV or PDF.
What is present value?
Present value (PV) is what money you will get in the future is worth today. A dollar today can be invested and grow, so a dollar in ten years is worth less than a dollar now. Present value tells you how much you would need to invest today, at a given rate, to end up with that future amount. This idea, the time value of money, is behind loans, bonds, pensions and almost every investment decision.
Present value formula
PV = FV ÷ (1 + i)n
- FV is the future amount;
- i is the interest rate per period, also called the discount rate;
- n is the number of periods.
Example: $1,000 in 10 years at 6% is worth $1,000 ÷ 1.0610 = $558.39 today. The difference, $441.61, is the interest the money would earn in between. These are the calculator's default inputs.
How the discount rate changes the present value
The higher the rate, the less a future amount is worth today. $1,000 received in 10 years:
| Discount rate | Present value |
|---|---|
| 2% | $820.35 |
| 4% | $675.56 |
| 6% | $558.39 |
| 8% | $463.19 |
| 10% | $385.54 |
Present value of an annuity
For a series of equal payments, an annuity, the present value is:
PV = PMT × (1 − (1 + i)−n) ÷ i
10 payments of $100 at the end of each year at 6% are worth $736.01 today. Made at the beginning of each year, an annuity due, they are worth $780.17, because each payment comes one period sooner. Multiply the formula by (1 + i) for payments at the beginning.
Lump sum or payments over time?
Present value is the fair way to compare money now with money later. Say a prize pays $800,000 today or $60,000 a year for 20 years. The payments add up to $1,200,000, but at a 5% rate they are worth only $747,733 today, so the lump sum is worth $52,267 more. At 4% the payments would be worth $815,420 and beat the lump sum, which is why the rate you choose matters so much. The same comparison works for a pension, a legal settlement or a structured payout.
Where present value is used
- Comparing a lump sum with payments over time, such as a lottery prize, a pension or a legal settlement.
- Valuing bonds, rental income or a business from the money it will bring in. The bond calculator prices a bond this way.
- Deciding whether an investment is worth its price today: the net present value (NPV) is the present value of what it brings in minus what it costs, and the IRR calculator finds the rate at which the NPV is zero.
- Working out how much to set aside today for a future goal.
Present value vs future value
They are the same calculation in opposite directions. Present value moves future money back to today; the future value calculator moves today's money forward. To solve for the rate, the payment or the number of periods instead, use the finance calculator.
How to calculate present value in Excel
Use =PV(rate, nper, pmt, [fv], [type]). Excel treats money you receive as positive and money you pay as negative, so enter the future amount as a negative number to get a positive result: =PV(6%, 10, 0, -1000) returns $558.39, and =PV(6%, 10, -100) returns $736.01. Set type to 1 for payments at the beginning of each period.