Discounting a future amount
Present value answers how much a known future cash flow is worth today at a fixed discount rate. A lump sum uses FV ÷ (1 + r)^n. An ordinary annuity is a payment at the end of each year: PMT × [1 − (1 + r)^−n] ÷ r. Compound interest grows a deposit forward; a savings-goal page solves the deposit needed to reach a target.
Ordinary-annuity PV = PMT × [1 − (1 + r)^−n] ÷ r
At 0%, lump-sum PV equals FV and annuity PV equals PMT × number of annual payments
Example
$10,000 due in 10 years at 5% has a present value of about $6,139.13. $1,000 paid at the end of each year for 10 years at 5% has a present value of about $7,721.73. An Investopedia ordinary-annuity illustration of $50,000 a year for 25 years at 6% is about $639,168.
What this discounting leaves out
Lump-sum timing may use fractional years. Ordinary-annuity mode requires a whole number of annual end-of-year payments. Monthly annuities, growing payments, taxes, and a rate that changes during the term sit outside the formula. Enter 0% to see undiscounted totals.