Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Present value of a lump sum
Simple and Analysis modes, with Future Value chosen in Analysis
- PV
- present value
- FV
- the future amount
- r
- rate per period: the yearly discount rate ÷ compounding periods per year
- n
- number of periods: years × compounding periods per year
Compounding is set to Annually, Semiannually, Quarterly or Monthly: 1, 2, 4 or 12 periods a year.
Source: Standard formula; no single publisher. The IRS (Internal Revenue Service) publishes factors for a fixed term in Table B. They equal 1 ÷ (1+r)^n to six decimals when Compounding is Annually, as 0.613913 does for 5.0% over 10 years [1].
Present value of a series of payments
Annuity and Analysis modes, with Series of Payments chosen in Analysis
- PV
- present value
- PMT
- payment per period
- r
- rate per payment period: (1 + yearly discount rate ÷ c)^(c ÷ p) - 1, with c compounding periods and p payments a year
- n
- number of payments: years × payments per year
Each payment arrives at the end of its period, the first one a period from now. At a 0% rate, PV = PMT × n.
Source: Standard formula; no single publisher. Agrees with the IRS's annuity example, $10,000 a year paid quarterly for 5 years at 2.6%, with Compounding Annually, at the example's four-decimal rounding [1].
Sources
- Department of the Treasury, Internal Revenue Service. 26 CFR 20.2031-7: Valuation of annuities, interests for life or term of years, and remainder or reversionary interests, paragraph (d)(6), Table B, and paragraph (d)(5)(iv), Example 4. eCFR, current as of October 1, 2026.
What this calculator does not cover
- This values one lump sum, or equal payments made at the end of each period. It does not handle payments at the start of each period, payments that grow, or a stream that starts years from now.
- It does not compute net present value across uneven cash flows, and it leaves out inflation and tax.
- A term that is not a whole number of periods gives a fractional count, such as 9.6 payments for 2.4 years paid quarterly. The formula uses that count as it stands. The schedule lists whole periods only, so it stops short of the last part period.
Sources checked on .