A dollar tomorrow is worth less than a dollar today — present value puts a number on how much less. This calculator discounts a future amount and a stream of periodic payments back to today at a given rate, and shows the discount factor applied to every period.

Inputs

End of period Beginning of period

Number of periods (N)1 to 1000 n

How many periods of payments remain.

Future value (FV)At the end $

The amount you expect to have at the last period.

Interest rate per period (I/Y)Percent, 6 means 6% %

Used to discount every cash flow back to today.

Payment per period (PMT)Negative to receive $

Paid every period, before or after interest as chosen above.

Result

Present value —

Total payments —

Total discount —

Discount schedule

Period Cash flow Discount factor Present value

How present value is calculated

Discounting reverses compounding. With a per-period rate i over N periods:

PV = (FV − PMT × ((1 + i)^N − 1) / i) / (1 + i)^N

The term in brackets removes the future value of the payment stream; the division brings the remainder back to today. Payments made at the beginning of each period are discounted one period less, so the result is slightly higher. At a zero rate the formula collapses to FV − PMT × N.

Worked example

You expect $3,108.93 in ten periods, receive $100 each period, and the discount rate is 6%:

Present value = $1,000.00
The $3,108.93 and the $100 payments together are worth exactly $1,000 today
Total discount = $2,108.93 — what you give up by waiting

This is the mirror image of future value: the same inputs that grow $1,000 into $3,108.93 reverse into $1,000 when discounted at the same rate. If the two calculators disagree, one of the rates or the timing is off.

Where present value is used

Comparing investments. Two projects with different payout schedules can be ranked by their present values at the same discount rate.
Loans and leases. The present value of the payment stream is what the obligation is worth today.
Retirement and annuities. A pension or annuity is a stream of future payments; its present value is what you would need today to fund it.
Capital budgeting. Net present value — present value minus cost — is the standard accept/reject test.

Choosing the discount rate

The rate is the return you could earn elsewhere at similar risk, not the rate you hope to earn. A higher rate shrinks the present value of distant cash flows sharply; a lower rate makes long-dated payments look more valuable. Because the choice of rate changes the answer, present value is only as good as the rate behind it.

Present value calculator FAQ

What is the difference between present value and future value?

They are inverses. Future value compounds today’s money forward; present value discounts tomorrow’s money back. Same rate, same periods, same payments — one undoes the other.

Why is the beginning-of-period result higher?

Payments at the beginning of a period arrive one period earlier, so they are discounted for one period less. The difference per period is small and grows with the rate and the horizon.

Can the present value be negative?

Yes, if the payments are large enough relative to the future amount — a stream of outflows can outweigh an inflow. The sign tells you the direction of the cash flow, not an error.

How many periods can I enter?

Up to 1,000, which covers monthly discounting for more than 80 years.

Related tools

Future Value Calculator — the reverse direction: grow today’s money forward.
ROI Calculator — return on an investment in percentage terms.
Payback Period Calculator — when the cash flows recover the initial outlay.