Present value

A later cash flow is worth less than the same cash today whenever money can earn a rate, because today's cash could have been earning that rate in the meantime. Present value undoes that growth. Divide the future amount by one plus the rate, once for every period of waiting, and you have the sum that would grow into the promise if the rate is actually earned. Raise the rate or lengthen the wait and today's worth falls. At a zero rate nothing is being undone, so present value equals the cash itself.

The lump-sum form is $PV = F(1 + r)^{-n}$, where $F$ is the amount due, $r$ the rate per period and $n$ the number of periods. A level end-of-period payment is the same identity stacked: each instalment is discounted on its own date and the present values are added. The present value calculator does both, using a nominal rate split across the compounding frequency. Six percent compounded monthly is half a percent a month for $12t$ months, not 6 percent applied once a year.

Net present value is the next step, not another name for the same number. Present value prices the inflows. The NPV calculator subtracts what you pay today to buy them. Mixing a monthly stream with an annual rate, or a real rate with nominal cash, is the usual way the figure comes out wrong by a few percent, which on a long stream is the whole decision. Time value of money is the long-form version of the same idea.