LaTeX
PV=PMT\frac{1-(1+r)^{-n}}{r}Variables
- PMT: payment
- r: rate per period
- n: payments
How to use this formula
Discounts equal end-of-period payments to a present value.
Important notes
- Beginning-of-period annuities require an additional factor 1+r.
- Taxes and fees are not included unless added to cash flows.
Quick example
A five-payment stream is discounted using the matching per-period rate.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Beginning-of-period annuities require an additional factor 1+r.
- For the Present Value of Ordinary Annuity, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Match the interest rate to the compounding period, convert percentages to decimals, and keep cash-flow timing consistent.
Worked example
A five-payment stream is discounted using the matching per-period rate.
Common mistakes
- When copying Present Value of Ordinary Annuity, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Present Value of Ordinary Annuity with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Present Value of Ordinary Annuity in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
PV=PMT\frac{1-(1+r)^{-n}}{r}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Present Value of Ordinary Annuity used for?
Discounts equal end-of-period payments to a present value.
Can I copy this formula as LaTeX?
Yes. Copy PV=PMT\frac{1-(1+r)^{-n}}{r} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.