ReckonBoxHow the present value calculator works
Present value is what money you receive in the future is worth today, given a rate you could otherwise earn on it. Enter a future lump sum, a stream of payments, or both, and this tool discounts them back to a figure in present money.
Compound interest runs one way; this runs the other. They're exact inverses, and the difference between them is the difference between "what will my savings become" and "what is this future money worth now".
The formulas, all of them
For a single future amount:
PV = FV / (1 + i)^n
For a stream of payments arriving at the end of each period, an ordinary annuity:
PV = (PMT/i)[1 - 1/(1+i)^n]
For payments arriving at the start of each period, an annuity due, multiply that by (1+i).
And combined, with a compounding frequency, as CalculatorSoup publishes it:
PV = FV/(1+r/m)^(mt) + (PMT/(r/m))[1 - 1/(1+r/m)^(mt)](1 + (r/m)T)
T is 0 for an ordinary annuity and 1 for an annuity due. That flag is doing real work, and it's the piece most tools bury behind a dropdown without explaining.
Timing is worth exactly one period
An annuity due is worth (1+i) times the ordinary version. Every payment arrives one period earlier, so every payment gets discounted one period less.
At 5% annually that's 5% more, on the whole stream. Rent is usually an annuity due, since you pay at the start of the month. A bond coupon is usually ordinary.
This tool prints what the other convention would have given, because picking the wrong one is a silent error: the number still looks reasonable.
A worked case
$10,000 received in ten years, plus $1,000 a year, discounted at 5% annually.
| Component | Present value |
|---|---|
| The $10,000 lump sum | $6,139.13 |
| Ten annual payments of $1,000 | $7,721.73 |
| Total present value | $13,860.86 |
| Nominal cash received | $20,000.00 |
| What waiting costs | $6,139.14 |
Thirty-one percent of the nominal amount evaporates purely from having to wait for it. That's not a fee or a loss; it's the value of not having the money now.
Discount the same lump sum forward at the same rate and you get $10,000 back exactly, which is the inverse relationship in one line.
The discount rate is the whole argument
Which rate you choose drives the answer more than any other input, and it is a judgement call, not something you look up. It usually stands for what the money could earn elsewhere at comparable risk.
Double it from 5% to 10% and the present value of a ten-year sum falls by roughly a third. So a present value quoted without its rate tells you almost nothing, and two people can compute honestly and disagree by a wide margin because they picked different rates.
Compounding frequency matters too, in a direction people find counterintuitive. Discounting monthly at the same nominal rate applies the discount more often than discounting annually does, so the present value comes out lower. This tool shows the periods and the rate per period so the mechanics are visible.
What this calculator does not do
It won't tell you whether to take a lump sum or a payment stream. That comparison depends on a rate only you can justify, plus tax, plus how certain the payments are, and any tool that returns a verdict there is hiding an assumption.
Uneven cash flows are out of scope. This handles a level payment and a single lump sum; a series of different amounts on different dates is an irregular cash flow problem.
Risk isn't modelled at all. The discount rate is the only place uncertainty enters, and it enters as a single number you chose.
Results are arithmetic on your inputs, not financial advice. For decisions about your money, speak to a licensed financial adviser. To run the relationship forwards, the compound interest calculator grows a balance with contributions, and the interest rate calculator recovers a rate from a payment stream.
Frequently asked questions
What is present value? Present value is what a sum of money received in the future is worth today, given a rate you could otherwise earn. The formula for a single amount is PV = FV / (1 + i)^n, where i is the rate per period and n the number of periods. It runs compounding backwards: $10,000 in ten years at 5% is $6,139.13 today.
What is the present value of an annuity? For payments at the end of each period it is PV = (PMT/i)[1 - 1/(1+i)^n]. For an annuity due, where payments arrive at the start of each period, multiply that by (1+i). CalculatorSoup publishes both, along with the combined version PV = FV/(1+r/m)^(mt) + (PMT/(r/m))[1 - 1/(1+r/m)^(mt)](1 + (r/m)T), where T is 0 for an ordinary annuity and 1 for an annuity due.
What is the difference between an ordinary annuity and an annuity due? When the payment arrives. An ordinary annuity pays at the end of each period and an annuity due at the start, so every payment in an annuity due is discounted one period less. That makes it worth exactly (1+i) times the ordinary version: at 5% annually, 5% more. Rent is usually an annuity due and a bond coupon is usually ordinary.
How is present value different from compound interest? It runs the other way. Compound interest asks what a balance grows into; present value asks what a future amount is worth now. The two are exact inverses, so discounting $6,139.13 forward at 5% for ten years returns $10,000. A savings question is a compounding question, and a "should I take the lump sum or the payments" question is a discounting one.
What discount rate should be used? That choice drives the answer more than anything else in the calculation, and it is a judgement rather than a lookup. It usually represents what the money could otherwise earn at comparable risk. Doubling the rate from 5% to 10% cuts the present value of a ten year sum by roughly a third, so a present value quoted without its rate says very little.
Does the compounding frequency change the present value? Yes, and it lowers it for a fixed future sum. Discounting monthly rather than annually at the same nominal rate applies the rate more often, so $10,000 in ten years at 5% is worth less discounted monthly than annually. This tool shows the periods and the rate per period so the arithmetic is visible.